| |
Years of technical
only explanations in trying to teach computer aided design (CADesign
)have been found by this author to be not very effective resulting
in digital future shock. Most digital based design applications in
the last twenty years have not reached beyond the dimensional boundaries
of paper based processes and their attending cultures and social structures.
Thus, this chapter takes a unique approach by presenting a digital
way of thinking and techniques for the digital based three dimensional
computer aided design process. So, we will begin with an introduction
to the digital way that includes digital ethics, responsibilities,
3D dimensional orientation and description of the differences between
paper and digital design processes.
The most difficult,
expensive, time consuming to develop, and important part of all digital
systems is the human part of the system. The human part of most digital
systems is usually defective or broken. Because of the lack of understanding
of digital technologies, most digital systems are applied in the same
way as the past information technologies they replace. The result
is the growth of digital systems being blocked by technically obsolete
constructs and old social structures of the past paper, radio and
video based analogue information systems. The human part of current
digital systems has yet to make the transition to digital based, interactive
networked information systems. An example of the inappropriate application
of current paper social structures to digital are the present copyright
and patent laws. Because of the nature of digital data, these
are difficult or impossible to enforce with regard to digital. Digital
data is physically easy to copy and modify. Ownership of digital data
can not be rigorously proved. Digital data costs almost nothing to
copy. If you share digital data with a friend, you still have it,
unlike an apple or loaf of bread. Your friend can easily add to the
data and modify the shared data. Because of the dependencies in the
complex world of digital data, the natural tendency is to share data
or be excluded from evolving systems. The more you share digital data,
the more there is. The more there is, the more it is used and the
more digital technology grows. An example of this phenomenon is the
great digital growth in the United States (US) in the 1980s. In 1981,
IBM introduced its personal computer (PC) for use in the home, office
and schools. Due to the open architecture of the IBM PC, the 1980's
saw an expansion in computer use as clones of the IBM PC made the
personal computer even more affordable. The number of personal computers
in use more than doubled from 2 million in 1981 to 5.5 million in
1982. Ten years later, 65 million PCs were being used. The growth
happened because of the freedom to share and modify digital data,
processes and technical information. All of the technical information
for the hardware and the source code for software was free and open.
It is a very simple idea -- if digital technology is open, can be
freely used, modified, and shared by everyone, then digital technology
will grow very quickly. This digital reality is in conflict with traditional
social structures that currently close digital technology by high
costs through copyrights, patent laws, and other forms of traditional
ownership.
| 0.2
Common Good Public License |
Digital technologies
and its effect on humans and their social structures should be of
the greatest value and interest to the scientist and academic person,
but receives little or no attention in comparison to technical issues.
Because digital technologies are based on global sharing of digital
information, those creating and using new digital technologies have
the obligation to support: digital freedom, human rights and a sustainable
future. Because digital computations of the personal computer are
predicted to equal capabilities of the human brain in the next twenty
years (The Age of Sprirtual Machines, Ray Kurzweil, Viking/Penguin
Group, New York (1999) ISBN 0-670-88217-8) a deeper commitment to
ethics and global openness by the creators and users of digital technologies
is required to secure a safe, stable future for all. The development
of digital technologies under the Common Good Public License (formerly
known as the Greater Good Public License - in short, CGPL - http://www.cgpl.org) agreement, for example, and
its three provisions where all developers and users agree to use the
technology to promote digital freedom, human rights and a sustainable
future, is not only possible but it is the digital future.
You are free to
use this text and any ideas contained here, if you agree to share
this knowledge freely and use it to promote human rights and a sustainable
future. Please use this text in a special way. The person reading
these words should doubt, question and reflect upon how their senses,
perception and reason may deceive them. The person learning the digital
way needs to learn to think in a very special and systematic way about
computers and other digital devices. The following are the three steps
in learning to think in this special way. You must walk these steps
many time before you will understand the digital way.
- First
- define digital.
A
person should carefully describe the nature of digital materials.
- Second
- understand digital processes.
A
person should try to understand the logic for the existence of digital
processes
stemming from the nature of digital materials.
- Third
- derive first principles of digital.
When
a person understands the nature of digital materials (size, weight,
speed,
and cost) and the nature and relationship of materials to processes,
it
is then possible by logical reasoning to reveal the first principles
in the
development
and application of digital devices and understand the
emerging
digital culture and social structures that arise from the use of
digital
devices. This special systematic way of thinking does not rely on
our
physical senses, but on complex logic sometimes called scientific
thought,
which requires "rigorous proof" of an idea.
An idea such as
the sun moves around the earth must be proven by rigorous
logic, observation and testing not just by simple observation. An
example of how we are deceived is shown by the fact that we can not
feel the movement of the earth. However we are told that the earth
is moving in an orbit around the sun, that the earth and its orbit
around the sun, the sun and the rest of our solar system are moving
at great speeds through space, but we can not feel the speed at which
we are moving or easily see any movement. We see clearly the sun moving
across the sky, and with no other information we would reason that
the sun revolves around the earth, but we are deceived. Currently
we see that a computer screen displays information that was in the
past displayed on a piece of paper, and we would reason that it is
the same as a piece of paper and we can use the computer in the same
way as we use paper, but we are deceived about computers and what
they have to offer. Fully understanding computers and the digital
way and what the future holds requires a person to doubt the current
use of computers and ask:
- What
are digital materials?
- What
is digital culture?
- What
are digital social structures / laws ?
- How
long does digital data last?
The answers
are not what you would expect. How much will change in future years
will surprise most everyone and may be difficult to deal with.
If
you have any questions, please mailto:carl@cgpl.org
The Computer Aided
Design (CAD) study in this chapter gives an overview of underlying
general principles concerning multi-dimensional modeling including
orientation, operations and applications. This chapter's text includes
the following:
- Discussion
about digital materials and processes.
- Presentation
of the Cartesian coordinate system.
- Handedness
and orientation in three dimensional space.
- Concepts of
the multidimensional digital design process.
- The differences
between: Visual Representation, Boundary Representation (B-rep),
Constructive Solid Geometry (CSG) Representation, Function Representation
(F-rep),
The first objective
is to provide a digital world view in the discussion and demonstration
of multidimensional modeling which shows the differences between paper
and digital material and processes. The second objective is to demonstrate
basic methods used in multidimensional modeling. The third objective
is the realization that the user interface must be as simple as possible
so as not to interfere with the creative thought process of the designer.
The fourth objective is to outline a set of basic functions for a
3D CAD modeling system which can be used as a specification for multidimensional
modeling systems of the future.
| 0.7
Paper Design Overview |
The paper based
design process for a new product model takes a long time. It involves
many people typically working in a large hierarchical social structure
divided into three functional design phases: conceptual design by
experts in a research group, working design by an engineering department,
and production design by the manufacturing department. Paper design
involves people with various levels of different skills and academic
degrees such as in physics and mathematics. It also involves highly
skilled drafters needing years of technical training. Drafting on
paper is the principal
process. Drafting is done for the purpose of control and verification
that the design will work . The actual verification of the design
is best done by producing a product prototype. This requires yet a
different set of highly skilled people. When the product is scheduled
for production it often needs modifications so it can be produced
effectively.
| 0.8
Digital Design Overview |
Digital design
based synthetic simulation allows levels of interactive design detailing
and verification not available in the physical prototyping processes.
A hierarchical structure involving many highly skilled people doing
many disparate tasks is not necessary. The long time from conceptual
to production designs is drastically reduced from years to months
and from months to days. The process is only hindered by the ease
of navigation in Cartesian space that imposes demands for a highly
interactive and yet simple, intuitive human interface. Digital designing
offers so much more than paper and physical processes, yet the change
over to digital design is very slow because of lack of understanding
and overcoming entrenched paper based hierarchical social structures
of the past millennia. There are still technical issues to be addressed.
However the development and implementation of multidimensional modeling
is more of a social problem than a technical problem.
Note:
At the end of the chapter there is a list of software resources and
exercises. Three dimensional visual spatial navigation and modeling
is understood through experience and reflection on that experience.
It is recommended that you use the HTML version on the CD with animated
GIFs and the free programs provided.
At
each new level of energy input to a given system, that system may
cross boundaries of discontinuities creating instabilities. The invention
of digital devices and the rate of technological advances stemming
from these devices are creating social discontinuities that often
do not allow for recognition of the capabilities or allow for the
full use of such digital technology in certain sectors. This
is especially true in CAD.
Sometimes
inventions do not flow out of previous inventions. This adds to the
confusion in transitioning to the new technology. The pencil did not
evolve into a computer. While both are tools that serve a common need
for human communication, one did not evolve from the other. A comparison
between pencil and a computer seems to hardly have any relevance because
there is such a great difference. The paper and pencil are very simple
objects and are easy to use for simple communications. Because of
these limitations, drafting, which relies heavily on the use of paper
and pencil is difficult, complex, slow and inaccurate compared to
computer based engineering and design practices. Although computer
based design and engineering has its own complexities that need to
be overcome, it is relatively easy, fast, precise and practically
unlimited in nature. Again a comparison between an imprecise analog
line drawn on paper and a digital model of a line on the windshield
of your computer design system is so great that a comparison should
seem to be irrelevant or even silly. However most people do not make
the realization that a line in the computer is dynamic: able to be
copied perfectly, rotated, shortened, lenghtened, divided, offset,
mirrored, arrayed, has no width yet carries sixteen decimal places
of accuracy. In fact, it is functionally alive; there is no
parallel on paper.
The
paper drafting process and procedures based on the simplicity of paper
and pencil have severe dimensional and dynamic limits in comparison
to the computer modeling process. Paper drafting is two dimensional
media. It fakes three dimensions through front/side/top projections
or 3/4 views drawn with illusive isometric perspective, or fake exploded
views. The skill and training requirements needed for designing using
drafting procedures are very high. Six years of math to be an engineer
plus two years of drafting classes equals a total of eight years of
training. The basic tools used in paper drafting procedure are very
simple in comparison to the computer design tools. However in application,
the engineering and design based drafting is far more complex, difficult
and slow to use in comparison to computer based engineering and design.
The paper drafting process is very inaccurate because of the imprecision
of the materials and the need for working to scale, the computation
of that scale and dimensions by hand-held calculator and the use of
complex geometrical projection drafting procedures required in faking
a reality of three dimensions. The computer drafting process where
the computer is used as a simple substitute for paper and pencil uses
the exact same procedures as the paper drafting process and is as
inaccurate and slow if not slower than paper drafting. The users of
a computer paper drafting system will say they are much faster using
paper and pencil in comparison to using a computer. The computer they
say slows them down and is too complex to set up and maintain. They
very often laugh and say that the computer is just a very expensive
electric eraser. They will admit that it is a little faster in the
creation of labels and drawings are cleaner and look better. The fact
is that if they use the computer as a substitute for paper, they are
quite correct in their observations and should limit the use of computers
in their operations and should continue to use their traditional drafting
processes. The typical computer drafting workstation includes
a electronic drawing pad, plotter, a hand-held calculator, pad of
scratch paper, pencils, technical pens, drafting board and all of
the other supporting equipment and tools to do cut and paste of paper
drawings. On the other hand a computer aided design workstation
requires only software, PC, mouse, keyboard and a plotter when the
output is paper drawings.
| 1.3 Paper Computers and CAD
|
A computer is a
very powerful general-purpose tool, that can be used as a simple substitute
for pencil and paper. The Macintosh computers were designed to be
easily used as a substitute for pencil and paper. So of course the
Macintosh by many of its users is seen as a typewriter and used only
as a typewriter for the sole purpose of making paper documents. Macintosh
users typically do not know how to share files or how to use any of
the advanced capabilities of a computer. In the same way, many current
computer aided design systems are actually computer aided drafting
systems. Their user interface has been designed to be similar to the
use of a piece of paper and like the Macintosh applied to drafting
as a simple substitute for paper and pencil using the drafting processes
and procedures that have been developed over the last 400 years. The
people who use computers as a substitute for paper and pencil have
no idea how to really use the powerful capabilities offered by computers.
That the use of
computers as a substitute for paper causes confusion between drafting
and multi-dimensional computer design is reflected in the understanding
of the acronym CAD itself. Many who use the paper processes for design
believe the acronym CAD stands for Computer Aided Drafting (CAD),
but the acronym stands for Computer Aided Design (CAD) as first claimed
by the United States Air Force materiel's lab. The users of CADrafting
do their calculations with a hand-held calculator and call what they
are doing drawings, and these drawings are as full of mistakes as
the paper drawings drawings that preceded them.. In comparison, the
users of CADesign do their calculations using the computer to create
geometric constructions through the view screen into multidimensional
space. The users of CADesign are not drafting and faking dimensions.
They are modelers modeling precise multidimensional, mathematical
models.
| 1.5 The Extinction of Drafting
|
Computer Aided
Design (CADesign) did not evolve from drafting even if both serve
as design tools and the processes are confused by most. Designing
with a computer by creating models in multidimensional space requires
very different procedures, processes and rules than traditional drafting.
The CADesign processes are as different from the drafting processes
as a pencil is from a computer. The CADesign system uses digital media
to create a precise mathematical model in multidimensional space and
then create a flat projection from that model in order to produce
an accurate set of paper drawings with a plotter. Yet many people
continue to use CADrafting which is only a substitute for paper and
pencil and nothing more and reject the computer's capabilities, dismissing
the advantages of multidimensional space as too complicated. However,
as the power of the PC is increasing, CADesign technology is prevailing,
particularly with a new generation of computer users, pointing to
the eventual extinction of CADrafting.
CADesign in contrast
to CADrafting is a multi-dimensional digital media, offering direct
manipulation of 3-dimensional objects. Models can be made interactive
by giving the viewer the ability to fly through buildings exploring
its design, or to zoom inside a machine examining the relationship
of its parts. Models can be animated moving them through a fourth
dimension - time. A designer or engineer using CADesign only needs
to learn a small set of simple rules in comparison to drafting. Because
all mathematical operations can be done visually through geometric
constructions, the designers and engineers do not need the extensive
formal training previously required. A person can become a master
designer or engineer in six months rather than eight years.
Most of the training
given in CADesign is almost always based on learning the user interface.
In reviewing thirty five CAD textbooks on Autodesk's AutoCAD software
application, each text book began by stating that the user should
consider the computer screen to be a piece of paper. None of the textbooks
gave anymore than a history of the development of AutoCAD commands.
None of the textbooks demonstrated how to solve necessary engineering
calculations by doing geometrical constructions. Most of the textbooks
consisted of exercises for each command, but they only dealt with
two dimensional applications. Yet none of the exercises took into
account the rules of drafting and the drafting specifications for
the creation of paper drawings. None of the textbooks offered a systematic
approach to creating models in Cartesian space and then being able
to use the models to create paper drawings.
| 1.8
CADesign, a Cyberspace Ship |
The computer screen
of a CADesign's workstation is not a piece of paper! It is the windshield
of a cyberspace ship - the face shield of a small personal virtual
jet ski surfing, probing, and exploring the vast virtual universe.
Understanding the true nature of the digital materials and processes
as practiced in CADesign systems is essential to making the most effective
use of these systems. CADesign is not merely a substitute for drawing
on paper. CADesign is a new digital media device. It is a multidimensional
modeling space that allows you to make simple virtual bit stream -
blocks, spheres, nuts, bolts, pistons, molecules, cells, so on - realities
that can evolve into complex virtual and synthetic life streams -
ever more complex assemblages of data. This digital flux will expand
our consciousness and create a network of synthetic awareness of the
world unlike anything we have ever known.
Only
a few people who are digitally literate have come to understand and
develop an intuition concerning the social impact of digital materials
and processes, but even they most often consider synthetic worlds
to be parallel worlds to the natural world with little connection
between the two. However the practice of CADesign demonstrates that
synthetic worlds are very much a part of the natural world and the
natural world will be greatly affected by synthetic objects created
with these systems. CADesign systems are the critical link, bridge
or transportation device that connects digital realities to the natural
world.
The
new digital structures are creating future shock. The confusion between
CADrafting and CADesign is an example of this future shock. Legal
ownership of digital materials, 0's and 1's, and their associative
digital data, bit streams and processes cannot be rigorously proven
or verified causing misunderstanding as to value. For example, Netscape,
though highly successful, never created a positive cash flow for its
investors. The failed dot coms caused financial instability of the
stock market. Digital bit streams are more illusive than water or
air, where only the ownership of the land through which they flow
can be proven by traditional law. Digital material and its attending
virtues are bringing to question the validity of ownership, and this
suggests that ownership should be replaced with stewardship and service.
The value of digital materials depends upon their use, and unlike
analog materials their uses are unlimited. Unlike the analog process
of copying, where the copy degrades from the original and the process
is thereby limited, the digital process of copying does not degrade
and costs very little in comparison to the analog process. The extreme
difference between the digital and analog processes is expressed in
the basic conflict between the idea of openly sharing digital information
and the concept of proprietary ownership. Currently, companies use
the CADesign process to create proprietary designs and patents on
which they depend to create value on the stock market. They have no
interest in sharing that information with anyone. Therefore most of
the software companies that provide CADesign systems have no interest
in their systems having any compatibility with any other systems.
| 1.11 Virtual Networked Organisations
|
In
the digital world no one has ownership and the idea of product is
being replaced with the idea of service. This is really not much different
than the actuality of business today. Most people who conduct business
do not own patent rights or copyrights but are simply providing a
service. The overwhelming efficiency and convenience of CADesign will
promote the development of direct manufacturing. Consider the following
future scenario. Choose an object that you want from swarms of cyberbody
information. The object will modify itself to suit your needs and
directly manufacture itself. Materials will be recycled. This will
be a reproduction service having little or nothing to do with ownership
of the original design, tooling and or production facilities. The
design and production processes will become self modifying. How then
can one judge who owns a patent or copyright to a design created by
automated processes. Businesses of the future will be digital structures
called Virtual Networked Organisations (VNOs), organic growth models
featuring no central control or job descriptions.
[ For further study on the subject of VNOs, please refer to the paper:
"Management and Virtual Decentralised Networks: The Linux Project"
by George N. Dafermos, First Monday, volume 6, number 11 (November
2001), URL: http://firstmonday.org/issues/issue6_11/dafermos/index.html
]
Because of its
application value to design and drafting, CADesign software applications
continue to be some of the most expensive and profitable personal
computer software in the world. The profit in CADesign software is
second only to operating system software. At the start of the PC revolution
in the United States, AutoCAD software by Autodesk became the de facto
standard for many years in personal computer computer aided design
software and was second to Microsoft in profit measured in billions
of dollars. Profit however is not the reason to study CADesign. Multidimensional
modeling and synthetic simulation are some of the most challenging
and important technologies in the field of computer software.
| 1.13
Control the Replicators |
The importance
of computer modeling / CADesign is only understood by a few people
who have been in the field of manufacturing and production involving
the application of numerical control (NC) machines or other digitally
controlled processes. Studies made about the development of flexible
automation show that multidimensional and accurate digital data and
speed of processing is the limiting factor in the design, development,
manufacturing and implementation of a cycle of new devices. The length
of this cycle was critical to the US Air Force who needed a new fighter
plane to fight a jungle war in Vietnam. The lead time was 5 to 7 years
for the development of a fighter. Acquiring the data needed for the
NC equipment and the associated tooling to assemble the fighter were
the bottleneck in development. It is this author's opinion and experience
that the big four companies of the US military industrial complex
have blocked the development of small, just in time manufacturing
units and flexible manufacturing, because this type of development
threatens their combined monopoly on the manufacturing of military
equipment. As the power of personal computers continues to increase,
so does the value of virtual models. Virtual models will quickly be
pushed to the higher level of synthetic models. Automatic digital
design agents capable of design verification and design modification
for conservation of materials will become available. Three dimensional
sub micro printing will create nano machines and thin film flexible
digital devices.
 |
The
current rapid prototype machines using only one type of material
will evolve to use many types of materials, and rapid prototyping
will turn into direct manufacturing. Laser Sintering will be
able to create solid 3D objects, layer by layer, from plastic,
metal, or ceramic powders that are "sintered" or fused using
CO2 laser energy. The inherent versatility of this technology
allows a broad range of advanced rapid prototyping and direct
or rapid manufacturing applications to be addressed. Objects
can be designed and made on demand when needed with this type
of replication. Copyright and patent laws from the centralized
point of view block the research and development of this type
of technology. Clearly new social paradigms are needed to allow
and support development of these emerging digital technologies. |
Modeling
systems of the future will not be used to create paper drawings but
the actual objects of design. The modeling systems will need to be
much more accurate than current systems and to be free for peer review
and modification.
| 2.0
Theoretical Orientation |
Theoretical orientation
includes the history of the Cartesian coordinate system, the basic
theoretical concepts behind the Cartesian modeling system, and definitions
of the Cartesian coordinate system. Also covered in this
section are a digital learning approach, para-solids modeling kernels,
Constructive Solid Geometry (CSG), and Function Representation (F-rep).
| 2.1 The Cartesian Coordinate
System |
The Cartesian coordinate
system is procedural method used to describe the dimensions of a synthetic
space. The Cartesian coordinate system is attributed to/documented
by Rene Descartes
(1596-1650).
Rene
Descartes
(1596-1650)
|
Descartes
is most famous for having written a relatively short work, Meditationes
de Prima Philosophia (Meditations On First Philosophy), published
in 1641, in which he provides a philosophical groundwork for
the development of the sciences. However, Descartes was a maverick,
a freelancer with no academic or political ties to universities.
Descartes radically asserted all existing knowledge rests on
the unstable foundation of Aristotelian physics based on our
senses, perception and reason, which deceive us. Cartesian physics
is a system of synthetic reasoning; knowledge starts with a
first principle and proceeds mathematically through a series
of deductions, reducing physics to mathematics. The properties
of bodies in Cartesian physics are measurable specifically on
ratio scales, and hence are subject to mathematical rendering.
The Cartesian philosophy is the logical referencing of quantitative
nodes of knowledge, establishing these quantitive nodes in a
procedural relationship to create a cellular system of thinking.
One should start by systematically doubting everything and find
the first principle of knowledge trusting only the procedures
of logical thought. |
| Descartes'
Cartesian philosophy of reference is expressed in the latin phase,
Cogito, ergo sum (l think, therefore I exist). This phrase is
the point of origin from which he derived the rest of the philosophy.
Descartes expressed Cartesian science in the establishment of
the first principle single point of origin from which he developed
procedures by which to study a three dimensional synthetic space
and three dimensional virtual objects inside that space, thus
linking geometry to algebra and physics to mathematics forever.
Descartes did so by defining the Point of Origin and procedurally
referencing it to three infinite lengths of cords called the coordinate
axis labeled X ,Y, Z axis, that are mutually perpendicular to
each other and bisect each other at the point of origin. The infinite
axis having equal divisions of negative and positive values which
originate from a single point of bisection at the point of origin.
Therefore the Point of Origin has a set of coordinate axis values
called coordinates of 0,0,0. Once the Point of Origin 0,0,0 has
been established along the three axis, this creates the synthetic
existence of an infinite grid of cube shaped cellular space called
the Cartesian Coordinate Space. This synthetic space allows for
the development of mathematical modeling and the study of three
dimensional virtual objects. Rene Descartes' quantitative philosophy
of synthetic cellular reasoning succeeded in overthrowing a qualitative
system of natural reasoning philosophy of Aristotelian physics
that was centuries old. With Cartesian space (X,Y,Z), Function
Representation (F-rep) - f (X,Y,Z,...N), and the ever increasing
computational power of computers, we are ready to remove the rectilinear
limits of virtual objects in Cartesian space and model dimensions
beyond our imagination. |
 |
The
natural process of learning involves associating new things to something
that is familiar or looks similar. Visually a line looks the same
on a piece of paper as it does on a computer screen. The comparison
of a line on a piece of paper and on a computer screen is the same
as the comparison of a person who is dead and a person who is alive.
Please do not think that you will save time by scanning the dead lines
from paper drawings into digital alive lines on a computer screen.
This is much like trying to raise the dead. Yes, all of the paper
drawings you have are a thing of the past and need to be made into
models. The results of scanner / raising the dead will be nightmarish
zombies creating manufacturing horror stories equal to the B grade
movie "Night of the Living Dead". Remember the letter D in the acronym
CAD is for Design, not drafting. Thinking about using the computer
screen as a piece of paper is approaching the computer from a 2D drafting
paradigm instead of 3D modeling, design and simulation paradigm. So
please resist the natural tendency to think of the the computer screen
as a piece of paper. Please think of the computer aided design system
as a cybership named CADesign and the screen, as a windscreen,
the face shield of CADesign through which you can travel the
vast reaches of multidimensional space. Refer to the CADesign's
process as modeling and the results as a model. A drawing is limited
2D lines and paper attempting to fake 3D. If you are drawing with
a computer then you are using a paper design process that does not
offer the advantages of the digital design processes. A person, who
is using a calculator instead of CADesign's systems, drawing
fake dimensions on a paper screen, is not clear on the basic concepts
of using digital technology and therefore cannot see nor use the incredible
mathematical intelligence of CADesign's systems that awaits
their fingertips. Design calculations can be done easily by using
constructive modeling (the intelligence of CADesign's systems)
in multidimensional space. By watching the calculations unfold before
your eyes, there it is on CADesign's windscreen if you dare
to explore constructive modeling solutions for a needed design calculation.
The use of constructive modeling on CADesign's windscreen is
a system of using math visually. The proper use of CADesign's systems
allows you to access CADesign's mathematical intelligence which
mentors you in proper design replacing years of tedious mathematical
training. CADesign's command and control systems has in line
mathematical functions for all other calculations that can not be
solved constructively. CADesign's sixteen place internal results
does not need to be rounded off for the human operator. The hand typed
input from the eight place display of a hand held calculator is some
kind of a cruel joke. A designer/engineer at a CADrafting workstation
(a CPU with multiple parallel processing floating point math units)
using a pencil, pad of paper and a hand held calculator for their
design calculations is sadly unaware of the joke.
The word "Para" means like something, but not really that something.
"Para Solid" modeling means its like solid modeling, but not solid
modeling. The base or core mathematical representation is not to be
confused with visual representation. Visual representations, wire
frame and surface polygonal meshes, are used to visualize the mathematical
representation. It is important to learn the difference between solid
constructive geometry, implicit surfaces, volume modeling and the
boundary representation polygon based procedures used by most CAD
systems. Early modeling systems were written complete with a user
interface, core processing and output routines by each company. However
many well known 3D CAD systems which claim to be "Solid Modelers"
are now constructed based on kernels obtained from third parties,
notably the ACIS (Spatial Technology, Inc.) and Parasolid (Unigraphics
Solutions, Inc.) kernels which only use some of the solid modeling
procedures. They typically do not retain any of the mathematical primitives
or history of procedures used, and the output from these kernels are
"polygonal meshes with holes" models. In fact, they are boundary representations,
not "solids". It is a fictitious stretch of marketing imagination
for most well known 3D CAD systems to use the term solid modeler and
to refer to the models created as solid models. The so called "solid
modeler" systems currently sold today are most likely not!. Please
note: ACIS and Parasolid kernels do allow provisions for the retention
of some type of procedural history. What that procedural history includes
is not clear and how the various companies implement the kernels is
not clear. A review of a recent release of one CAD system shows that
the " para solid models" can be edited. This implementation of Parasolid
shows a history tree of operations. Mathematical representation by
the "para solid" model kernels are improving, but the models are still
polygonal surface models closely tied to the visual representation
of the surface. However because these improvements are not open for
review, no one can understand how good they are. Furthermore if they
are closed systems, they can not be compatible with other CAD systems.
| 2.4
Open Procedural History |
An open procedural
history or list of commands to create an entity is usually much more
compact than the completed model and is extremely important to the
migration of digital data to other systems. Furthermore, if constructed
properly, it contains all the information that is needed for the final
geometry, including the representations of solidity and volumetrics.
It has long been known that such a historical list (actually a tree)
of commands is a valid model in its own right. The highly accurate
input that forms an entity's history that can be used to adjust the
level of detail, and answer the same sort of questions as the final
model provides (e.g., is this point inside or outside the solid?)
without actually constructing a boundary model for visual representation
at all. The substantially significant advantages in the use of
procedural history include providing a robust data structure providing
stability and verifiable process procedure and accuracy. Making a
boundary based representation model is complicated, and inevitably
inaccuracies creep in; in particular, the edges of a boundary
model often deviate slightly from the surfaces that they are bounding.
It is extremely difficult to stop these errors from affecting subsequent
calculations. On the other hand, working directly from the history
with what we will refer to as a Constructive Solid Geometry (CSG)
model, we are using the 'raw ' input and geometry. The ACIS and Parasolid
modeling kernels of course use mathematical functions; however it
is anyone's guess what functions are used because the source code
is not open for peer review. Furthermore the vendors implement the
kernels differently. Most do not retain any history at all, but fool
their clients into thinking they are using "solids" and CSG when they
are not. Therefore without a history or a CGS procedural tree, most
of the models being created on most current modeling systems are dependent
on the system that created them and are subject to being lost when
any of the complex parts of the original system change. It is a sad
fact that most all of the 3D models without a history of procedures
or originating input could be useless within as little as one to five
years and, without a doubt, will not have any value in fifty.
A procedural history of the construction of 3D models is of key importance
to verify your 3D models, share your models between systems and be
able to migrate the 3D models to future systems, thus protecting your
investment of time and labor in creating the models.
In the diagram
below, we can see the six CSG primitives, upon which Boolean operations
can be performed in CADesign.
| 2.5
Constructive Solid Geometry (CSG) |
Solid modeling
programs that have a proven set of mathematical operations and
retain a history of the mathematical operations and other procedures
stored in a CSG tree (that can be traversed and modified by the
users to verify the results) are recommended for many reasons.
The following is an example of the need to verify data using a
CSG tree. The three-quarter view and plan view diagrams below
of a CSG tree of a solid model show the model's primitives on
a round pad, and the Boolean operations performed on the primitives
are shown on a binary fork in the branches of the CSG tree. There
are a total of nine primitives and eight Boolean operations.
 
The
model's primitives are made of eight cylinders and one cube. Starting
from the top left moving to the right and down in the bottom left
diagram, the following describes the union and subtraction of
the first four primitives. In the first two sets of cylinders
with one horizontal and one vertical cylinder in each set, the
horizontal and vertical cylinders in each set are joined together
with a union operation to form two solid cylindrical plus symbols.
The small diameter shape is subtracted from the larger diameter
shape to form a hollow shape that resembles two sections of pipe
cut and welded together to form a plus symbol.
 
Theoretically
with a proven set of given mathematical operations, changing the
order of operations will always give the same mathematical results.
However if you look closely at the hidden view diagrams above
of just the top part of the CSG tree that has five primitives
and four Boolean operations, you will notice that the one on the
left has different operations from the one on the right. The one
on the left has two Unions (U) and a Subtraction (S), whereas
the one on the right has two subtractions and one union, in the
first three operations. You will also notice the last/fourth operation
(at the bottom of the tree), a subtraction of a cylinder, leaves
an opening allowing you to see inside both of them. You will see
the hidden view of the one on the right confirms that the model
is not correct. Using the wire frame views of the models, you
will be able to see in the diagram below that the error actually
starts with the union operation previous to this one, but you
cannot see the error in the hidden view above. The modeling operations
of the one on the right is a more natural order of operations,
using the subtraction operations first to create horizontal and
vertical sections of pipe and then a union to join them together.
However, this order of operations creates an error as seen above.
Four
wire frame visualizations of solid models are shown above. The
first wire frame visualization of two tubes welded together starting
at the top left of the diagram is the result of subtraction of
a two small cylinders from two large cylinders creating two tubes
followed by the union of the two tubes into the geometric shape
of a plus, and the wire frame visualization clearly shows an error.
The second wire frame at the top right shows the subtraction of
a fifth large cylinder through the center of the plus shape and
clearly shows that subsequent operations carry the error forward,
and the error grows. The third wire frame visualization at the
bottom left is the result of the union operation of two large
cylinders and two small cylinders into a large and small plus
shape followed by the subtraction of the small plus shape from
the large shape, and it is clear there is no error. The fourth
wire frame view, bottom right, is the result of the subtraction
through the center of the plus shape by a large cylinder and clearly
shows that there is no error. Again this type of error due to
change in order of procedures is clearly very wrong. The software
is quite flawed. In the future world of direct manufacturing,
this type of error will be unacceptable and must be discovered
by design checking agents.
Note: Do not assume your modeling to be accurate. The example
above shows that without understanding complex mathematics, you
can visually see the error in the model. The power to visually
check complex mathematical models is one of the greatest benefits
of using CADesign. The solid models in the examples above
were created using AutoCAD Rel. 12 software by AutoDesk with Advance
Modeling Extensions (AME). AME is the solid modeling extension
of AutoCAD Rel. 12 and was one of the very few commercially available
solid modeling programs. AME and the CSG tree were dropped by
AutoDesk in Rel. 13. However, AutoDesk still claims that AutoCAD
Rel. 13 and beyond are "Solid Modelers" and that simply is not
true in this author's opinion.
| 2.7 Function Representation
( F-rep) |
HyperFun Project
(http://www.hyperfun.org) is a free software
development project for functionally based shape modeling, visualization
and animation. The project is based on a so-called function representation
(F-rep) (http://wwwcis.k.hosei.ac.jp/~F-rep/
)of geometric objects and supporting software tools built around
the HyperFun language. In F-rep, complex geometric objects are
constructed using simple ones (primitives) and operations on them.
Any object in three-dimensional space is defined by a function
of point coordinates F(x,y,z). This continuous real-valued function
is positive inside the object, negative outside, and takes zero
value on its surface. Similarly, a multidimensional object is
defined by a function of several variables F(x1, x2, x3, ...,
xn). For example, an object changing in time can be defined by
F(x,y,z,t) with t representing time. In HyperFun, the functional
expressions are built with using conventional arithmetic and relational
operators, standard functions, built-in special geometric transformations
and F-rep library functions.
HyperFun
is the next step in CADesign development, as it also allows the
mathematical definition of any number of attributes of an object
such as materials, color, texture, hardness, softness and so on.
In creation of a CAD system with HyperFun, the mathematical modeling
will be retained apart from the visual representation.
Mathematical representation being separated from visual representation
and the processes open allow the mathematical representation to
be done on any platform now or in the future. HyperFun has been
in academic research and development for many years, but the application
side of development has just started. At present, HyperFun modeling
tools are still limited. There is not at this time a robust user
interface available. However development plans to create synthetic
CAD are underway and actual development should start soon.
| 3.0
Technical Orientation |
In
this section, we will discuss technical issues such as the definition
of the basic elements of a CADesign system, CAD models,
normal / natural orientation, mirror writing, CADesign
conventions in Cartesian space, wire model viewing, User Coordinate
System (UCS) icon.
A
robust computer based modeling system creates a mathematical model
not a drawing. Therefore, you need the latest and greatest computer
you can lay your hands on. A plotter is necessary to output paper
drawings. You should always have a small printer for data
dumps to check files and operations. Do not purchase a tablet.
You only need a keyboard and a mouse. High resolution screens
are not recommended, because the lines on the hi-res screen become
very thin and cause eye strain. I recommend the Linux operating
system and Varkon CAD software (http://www.microform.se)
as your best purchase. For rendering software, POV-Ray (http://www.povray.org)
is great. However it uses the left hand rule Y up, but uses the
right hand rule for rotation. You need to set up a transformation
of the data to use POV-Ray with your CADesign models which
will be right hand rule Z up. A review of Linux CAD showed it
to be extremely poor. Also, get a really good chair and make sure
you have good support for your arms.
 |
A
model, such as Sazaedo shown in the image to the left, is
made up of objects which are made from blocks which contain
entities. Entities are the basic primitives of the system
used to construct blocks and objects. Depending on what
are the basic primitives provided by a given CAD system,
entities might be points, lines, arcs , circles. There is
no standard convention for the naming of different elements
used in a given modeling system other than the naming conventions
of the Cartesian coordinate system. A point is a set of
X,Y,Z coordinates. A line has two points, a start point
and an end point; so it has direction and rotation; therefore
a line is a vector. An arc can be defined by a start point,
midpoint, end point and has a direction of rotation around
the center point not to be confused with the midpoint. A
circle has a center point and a distance. A polyline has
an unknown number of points that define both lines and arcs.
Polylines can be open or closed entities. If a polyline
is a closed entity, it can be extruded into a solid object.
Other basic entities are 3D faces, polygons and polymeshes.
Only three serious CAD systems have higher level CSG entities.
There are several experimental CAD systems that use higher
level function representation entities. From blocks or groups
of entities objects are created. In the Sazaedo model, the
compound complex shape of the lower roof could not be created
with CSG primitives. Also the spiraling over hanging roof
and internal ramp could not be created with CSG primitives,
because they also have compound complex shapes. Compound
complex shapes have surfaces that move in all three directions
(X, Y and Z)at once. That is to say that the X, Y
and Z values for any given set of points on the surface
will be different. All other parts of the model including
the top roof are CSG based entities. |
IGES (Initial Graphics Exchange Standard) and STEP (International
Standard for the Exchange of Product Model Data) are standards
for the sharing of modeling data. However they are closed standards
and, in the IGES case, limited and, in the STEP case, not implemented.
So there is no standard data file format used in the CAD industry
for accurate three dimensional mathematical (CSG) models which
can be used to transmit the logical structure of the model,
but only disconnected surface data. The Sazaedo model is
a historical digital preservation work. Therefore, mathematical
definitions, accuracy of the model and a history of the logical
structure of the building are important information from the historical
preservation viewpoint. Only the CSG based entities will
be able to survive over time in the current CADesign environment.
The AutoCAD DXF, a DIF type file format, that has become a de
facto standard for the export and import of three dimensional
polygon surfaces. The DIF file format is type of binary file format.
It is binary in that it has two lines of text for each data record.
The first line of text is a code that tells what type of data
is in the second line of text. Examples: Code 0 is the
start of a new entity. Code 10 is the start point of a line. Code
11 is the end point of a line. Most CAD files have data tables
of various settings for the operation of the system. The settings
necessary to setup AutoCAD for various applications can be extensive.
AutoCAD takes 250 keystrokes for the average setup of a given
application.
| 3.3
Normal / Natural Orientation |
In
theory we can define and use any orientation for modeling because
mathematical transformations are so simple and easy to do. Mathematical
theorists and some computer scientists insist orientation makes
no difference if the orientation is first defined. This is true
in theory but not in practice. Usage reveals that humans naturally
establish one normal orientation and can not think and work in
different orientations without experiencing confusion and making
mistakes. The use of orientations other than the normal orientation
in theoretical work obscures understanding and has even been used
as a form of encryption.
Our
hands are mirrored structures of each other, and yet there are
only a few exceptional people who can easily handle or adjust
to a stated orientation were the input or output of a system is
mirrored and rotated without making mistakes. It is interesting
to note that at an early age some children are naturally ambidextrous
and will easily handle writing with both hands and can mirror
write with either hand. To read what they have written, one must
hold the writing up to a mirror. However the children see no difference
at all, until it is pointed out to them and they are taught the
difference. Leonardo Da Vinci, an Italian Renaissance artist persecuted
for his knowledge and creative ideas, protected himself by keeping
his notes and journals from being easily read by mirror reading
and writing.
| 3.4
Mirror Writing Exercise |
To understand
how important the use of proper natural / normal orientation is
please take out a piece of paper and pencil try doing the following
tasks. First, try writing with your left hand if your a right
handed person. If you are left handed person, you do not need
to do this because you live in a world of devices created for
only right handed people. Now please try some mirror writing with
both the left hand and right hand for a few minutes. Once you
have tried the ambidextrous exercises, you will understand how
easy it is to get confused and how hard it is to work in a different
orientation. When possible, it would be better if we all work
with an established and agreed upon orientation, because the confusion
in trying to use different orientations is very great.
| 3.5 CADesign Orientation
Defined |
The orientation
in this chapter on modeling systems uses the Cartesian Coordinate
System having X, Y and Z axis with normal / natural orientation.
Normal / natural orientation is right handed where: the X axis
is positive movement to your right, the Y axis is positive movement
to the left , XY axis create a plane referred to as "the plane"
or "the ground plane" that is normal to the pull of gravity, and the Z axes is positive movement in the upward direction,
having vertical orientation to the pull of the gravity of the
earth and where the positive Z direction is against gravity. This
is the normal and natural orientation used in drafting, and CADesign,
because it is the orientation used in the fields of aviation,
engineering, architecture and manufacturing for the last four
centuries.
Unfortunately
some people do not have the ability to visualize wire frames images
in 3D at all. Working on wire frame images from the bottom view
is not recommended, because it causes visual confusion as we shall
see below. In working with wire frame, one should use 3/4
views, which are 3D views, for designing and editing. Those who
attempt to design in "plan views" (views from the top) or
"elevation views" (views from the side) are not working in 3D,
but rather in 2D. They will have difficulty selecting a
vertex, because they will not be able to tell if the vertex is
the one near to them or far from them. However, plan and elevation
views are useful for checking the model. The following example
shows the visual problems associated with viewing a 3/4 view wire
frame.
Which wire frame view
is from the top and which is from the bottom?
|
The
two images to the right and the left are different views
of a single 3D model visualized in wire frame. The two views
are of a rectangular box that is 4 x 5 x 6 units in size
that is a 3/4 view from the -1x -1y +1z octant reveling
the front, top and left hand side and a 3/4 view of the
same model from the bottom -1x, -1y, -1z. Please note: If
the model were a cube instead of a rectangle shown in
3/4 views from the top (+1z) and from the bottom (-1z),
we would see exactly the image. Therefore we would not be
able to tell the top of a cube from the bottom of a cube.
This problem is solved by using an icon to give visual indication
of orientation. |
|
Proper normal orientation is both the visual
and theoretical frame work on which you create a model. Modeling
with wire frame visualizations of complex mathematical
models is confusing at best and not even possible, if a standard
normal orientation and some type of visual cue for orientation
is not used. The "User Icon" is a dynamic symbol that is a visual
cue for the user as to the orientation of the User Coordinate
System relative to the World Coordinate System, the model and
the user's view. The User Icon indicates the location of 0,0,0
or the point of origin for the User Coordinate System, the general
orientation of the User Coordinate System and the positive and
negative orientation of the Z axis in relation to the screen as
shown below. Typically the User Icon is not used in computer drafting
which is 2D . This is unfortunate because the ability to have
access to a temporary point of origin / a user origin point is
extremely useful in designing in 2D. The default state for the
User Icon in AutoCAD is "on". It has been by the
author's experience that 95% of CAD installations do not use the
User Icon; it is turned off, as the users do not understand its
function.
A 3D Designer Must Use
a UCS Icon
|
The
addition of a coordinate icon helps. Now, can you tell which
wire frame is being viewed from the top and the bottom?
If you can not, that is OK because you can train yourself
to be able to see wire frame 3/4 views in 3D. A designer
can not design in 3D if he does not turn on the coordinate
icon feature. Please note several things about the coordinate
icon. 1 - This icon displays a W and that means it is in
the world coordinate view. 2 - There are small tick marks
at the intersection of the two arrows; this means that the
icon is on the origin point. 3 - In the left hand view you
will notice that two lines are missing from the icon that
form a square in the view on the right; this means that
Z is pointing away from you. |
|
Has the
visual cues of the User Icon helped you to tell which wire frame
you are viewing from the bottom? Working on wire frame
images from the bottom view is not recommended, because it impairs
the user's ability to visualize the 3D wire frame model without
confusion.
Below are images that show only
six of the possible eight states of the User Icon's visual cues.
Two images are missing. Which ones are missing? Can you list all
eight states of the UCS icon? Read the three numbered statements
above again very carefully and you should be able to figure it
out.
| 3.9
Normal Orientation Exercise |
Three points
define a plane, a point and a line define a plane, and two lines
define a plane - are basic Euclidean axioms used in plane geometry.
Using the axiom two lines define a plane, we will create two 3D
models of the X, Y and Z axis of the Cartesian system - one with
a sheet of paper and the second with our right hand.
 |
1st
model
Take out a sheet of paper and thin wooden pencil. Now place
a point in the middle of the paper and label it O for origin.
Now draw a line from the origin point in the direction to
your right and label it X. Now draw a second line from the
origin point perpendicular to the first line in the forward
direction and label it Y. With these two perpendicular lines,
the first plane of the Cartesian system called "the plane"
is made. The term "the plane" always refers to the X, Y
plane or ground plane that is normal to the pull of gravity.
Now finish the representation by piercing your paper from
the back side at the origin with the point of your pencil
pointing upwards from the front surface of the paper normal
to "the plane". Please be careful - but look at the
paper with the point of the pencil pointing toward you so
it looks like the image to the left. In drafting,
this is called the default view or unless otherwise noted
the top down or "plan view" of "the plane". You might think
of this view as a map or a layout of the ground plane with
you in the center. This is the creator orientation
or "God Orientation". Place this model in your
left hand and create the second model. |
2nd
model
Now, hang your right hand downward with hand open and your
fingers pointing toward the ground plane. Next, rotate your
wrist so that the palm of your hand is facing in the forward
direction. Bend your right arm at your elbow 90 degrees so
that the palm of your hand is now facing upwards. Your right
hand and your thumb should be pointing in the positive direction
of the X axis or movement to the right and your index finger
is pointing in the positive Y axis or pointing forward. Now,
bend the third finger upward. It is now pointing in the Z
axis. Rotate the right arm at the elbow so your right
hand is directly in front of you just level with your elbow
and keeping your right hand as shown in the image. In
3D design, this is "the view", "the artists view" or in drafting
"the three quarter view". "The view" is the normal viewing
of real objects that is the most common view experienced by
people. It is a view of an object from a natural body position
for normal people. Now move and rotate the paper model
to a position that is the same orientation as your right hand.
This is the "Right Hand Rule". |
 |
The above 3D models, one with paper and pencil and the other with
the right hand, are anthropomorphic based orientation for 3D modeling
and viewing - that is most efficient for humans. In fact,
if you do not use this view, you probably will not be able to
model in 3D. This orientation is called "the right hand
rule" with the normal natural orientation of Z up (Zup). However
Zup is the not the natural orientation for some people
like programmers. They work visually in a virtual world
of a computer screen where the forward movement of the mouse in
the real world is transferred to an upward movement of the mouse
cursor. So the natural orientation for them is Y up (Yup).
The difference in orientation between the Yup people and the Zup
people causes conflict. Orientation confusion in the real world
where gravity is a serious matter can lead to serious mistakes.
| 3.10
Virtual World Orientation |
Virtual world orientations are in conflict with the real world.
Unfortunately the orientations used in virtual worlds are not
just the relatively simple Zup Yup conflict of a 90 degree rotation,
but the virtual orientation is often mirrored from right to left
as well. Programmers who spend most of their time viewing and
navigating the abstract virtual world of cyberspace and very little
time building physical things in the real world of gravity are
not aware of right handed orientation or the need for a person
modeling to read wire frame models with normal views that match
aviation and engineering standards. Such programmers have written
all of the basic Open GL libraries (http://www.opengl.org) with the virtual world
orientation of left hand rule and Y up. Novice programmers who
are not aware of the problem will of course write simple programs
using the the left hand rule Y up orientation of the Open GL libraries.
A very famous program, POV-Ray, uses the left hand rule Y up orientation
and the right hand rule for vector rotation. VRML (Virtual Reality
Modeling Langauage) uses the orientation of right hand rule and
Y up, and the HyperFun program began life with the left hand rule
Y up orientation. HyperFun, looking toward synthetic simulation,
did not want to be in conflict with the real world and modified
their orientation. The Y up (Yup) or Z up (Zup) problem is the
most difficult to change in computer science because all the books
about Open GL talk about the Z buffer as a depth buffer, which
has become standard nomenclature for the virtual world. Open GL
libraries were given the orientation left hand rule with X as
width, Z as depth and Y as vertical height. These alternate views
are placing serious barriers to the visual bridge between the
real and virtual worlds and causing a great deal of disorientation
and confusion. Mirrored and rotated systems, including VRML standard
language and POV-Ray, come from not trying to find a first principle
with regard to normal orientation in the real world. People creating
such systems usually start out by not being aware that their virtual
world orientation is in conflict with real world orientation conventions
of the last 400 years in engineering, manufacturing, and aviation.
Programmers continue to use the left hand rule which is a mirror
of the right hand rule and/or a Yup orientation which is a 90
degree around the X axis from the real world normal orientation
of Zup.
The following is a quote from the POV-Ray web site:
"there is so much controversy about the right hand rule we decided
to use the left hand rule"
The X, Y axis
divides a given space into four sections, called quadrants. The
addition of the Z axis divides the quadrants to create octants.
|
If
we pick a point O as origin and draw two perpendicular
lines through the origin, we create "the plane." The
two lines are labeled X and Y axis. The term "the plane"
always refers to the X, Y plane or ground plane that
is said to be horizontal to or normal to the pull of
gravity. In the practice of drafting, the default view
shown to the left is the view from the top down or "plan
view" of "the plane." You might think of the plan view
as a layout or a map of the ground plane. The plane's
X, Y axis create four divisions of coordinate space
called the "quadrants." The quadrants are named for
their signs. The 1st quadrant is called the plus plus
quadrant (+X +Y axis). Proceeding in a counter clockwise
rotation, the 2nd quadrant is the minus plus quadrant
(-X +Y axis). The 3rd quadrant is the minus minus quadrant
(-X -Y axis) and the 4th quadrant is the plus minus
quadrant (+X -Y axis). A move to the right is in the
positive direction of X. A move to the left is in the
negative direction of X. A move forward is in the positive
direction of Y. A move backward is in the negative direction
of Y. |
| The
third axis, the Z axis, is added mutually perpendicular
through the point of origin of the X, Y axis. The a third
dimension Z is know as height or elevation in aviation.
The Z axis creates eight divisions of three dimensional
space called "octants." The positive direction of the
Z axis is up against the pull of gravity. Adding the Z
axis defines two more datum planes, the X, Z and the Y,
Z. When viewing these datum planes from a perpendicular
angle to the surface of the planes, the views are refereed
to as plan elevation views in the fields of engineering,
architecture and aviation. The figure to the right showing
all of the octants is known as a 3/4 view. Now we have
created a synthetic space, and every point in that space
has a unique triplet of cartesian coordinates labeled
as X, Y, Z . It is understood that if given a list of
three numbers, they are the Cartesian coordinates X, Y,
Z - - and they are used to determine a point in
Cartesian space applying a number as movement in space
along X, Y, Z axis. The 1st octant is +X +Y +Z. The 2nd
octant is -X +Y +Z. The 3rd octant is -X -Y +Z. The 4th
octant is +X -Y +Z. The 5th octant is +X +Y -Z.
The 6th octant is -X +Y -Z. The 7th octant is -X -Y -Z.
The 8th octant is +X -Y -Z. |
 |
| 4.0
Cartesian's Navigation Systems |
In this section
we discuss the subject of Cartesian navigation or viewing in-depth.
Examples below will show you how to view and change views of multidimensional
models in the virtual space created by the Cartesian coordinate space
system on the windscreen of your computer modeling system. ("Cartesian's
windscreen" where Cartesian is the name of a new imaginary
multidimensional spacecraft to be constructed.) We also present an
imaginary user interface to describe the subject of viewing in-depth
in the text below, as if it were an existing command where the use
of two letter acronyms is the keyboard entry which brings on screen
"Cartesian's" visual interactive interface for the command
mode. The ease and skill with which one can view the development of
a 3D model is an essential part of being able to model in Cartesian
space. A person's modeling ability is only limited by their ability
to navigate Cartesian space. Exploration and development of effective
navigational systems for Cartesian space has just begun. The complete
user control and ease of navigation in Cartesian space is the most
important aspect of multidimensional modeling.
We will begin with
an outline of all of the parts necessary for a robust Cartesian based
navigation system and then discuss the addition of a multidimensional
interface to navigation systems. Modeling systems must define and
keep track of at least two Cartesian coordinate systems, the world
and a user view. Most robust systems track and use at least four to
five different types of coordinate systems:
- World coordinates
- User view coordinates
- User or creation
coordinates
- Entities coordinates
- Groups of entities
coordinates
| 4.2
World Coordinate System (1) |
The
World Coordinate System is a single point of origin / base / handle
/ for the entire model and for the other coordinate systems. However
it is possible to create a simple system using only World and User
View Coordinate System(s). An example of this type of system is the
HyperFun polygonizer; such systems most usually depend on mathematical
definitions and are important teaching tools that provide an intuitive
feel for the relationship between math, geometry, programming and
computer visualizations. These types of systems are not useful for
modeling large complex objects or designs, because they are text editor
based. Viewing from only one View Point (VP) and the point of focus
or the View Target (VT) will allow us to easily see and verify the
results editing a single simple object using a text editor, as shown
in the HyperFun example below. To do visual based editing
rather than text based editing, one needs the other coordinate systems
as well.
HyperFun (http://www.hyperfun.org) is a simple system
of navigation for simple constructions. However, in concept, the system
can mathematically model any level of detail.
Text File
|
HyperFun
uses one and a half (1 1/2) coordinate systems. The world
coordinate system is almost the same as the the view target
(VT) or point of interest. The user can not move the VT or
point of interest and therefore is unaware of it. Only the
user view point can be moved by the user.
 |
VT
- point of interest can not be moved. This system can
not be used for large models with many objects. The text
file is shown to the left. Next to that at the command
prompt, the program is called by "hfp txt.hf -g 35" and
the image of the model appears in the foremost screen
shot. The user view can be rotated and zoomed with the
mouse. |
The
VT (point of view) is just off center from the world coordinate
system so that when the user view is rotated around a sphere,
some movement is able to be detected due to this slight offset.
|
The User View
Coordinate System is usually defined by one point, a direction or
point of interest and rotation that creates a cone and plane of view.
This is needed so that the user can change views and work from various
viewing angles. The editing of a single object can be done interactively
on your windscreen using the rendered visualizations of the object.
However when you use the visualization to edit even a single simple
object, it is done much more efficiently with the use of wire frame
visualizations (X-ray vision) rather than solid rendered visualizations.
While seated at Cartesian's controls, you can issue a command
for a re-scanning of the mathematical model. You can either use normal
vision and view the solid object, or you can give yourself Superman's
X-ray vision and render the Cartesian object transparent so that you
can see all boundary points and edges.
solid visualization |
X-ray visualization |
| 4.4
Superman's X-ray Vision |
A 3/4 view from 225 degree & 35.8 degree
|
Using
X-ray vision provided by Cartesian's windscreen conveniently
and efficiently allows you to make interactive mathematical
modifications to the object. Cartesian's digital agents
do the calculations for you. However, when you use X-ray vision,
you are using a very unnatural view, and, as shown to the left,
certain X-ray viewing angles (even simple ones) can be very
confusing and almost impossible to utilize. The image on the
left is a wire frame model of 3D cube of 5x,5y,5z units. It
looks like a flat 2D six sided figure. Can you visualize the
image in 3D and see it as a cube.? A solution as mentioned before
is the use of a user icon. However it is very hard to read upside
down, and with many complex models the icon becomes difficult
to use. The icon helps but by itself alone is not a good solution.
Therefore it is necessary (when using X-ray vision to edit objects)
to be able to easily understand your orientation to the objects
and the surface and distance relationships between the objects
being viewed. |
| 4.5 Autonomic Autopilot Controls |
|
Cartesian's
autonomic autopilot controls will
have autonomic movements, surface probing , and visual acuity
systems with standard tele-transport positioning portals. We
will describe only two of the proposed navigational controls
all ready proven to aid your visualization processing of wire
frame models. One is the use of autonomic movements or (very
slight rhythmic real time changes in the user view). All living
creatures have continuous autonomic movements that aid the creature's
perception. The second is the use of standard View Points (VP)
so that you may instantly tele-transport to a position in Cartesian
space. Below
are the proposed four standard 3/4 views for modeling in three
dimensions. The first view is "the view" V1 shown on the left.
This is the approximate view point of a person viewing an object
in their right hand with: elbow bent at a 90 degree angle, the
palm up, hand open, the front of the object aligned with the
X axis of the thumb, the arm rotated so the object is directly
in front of the person's waist.
- View 1 (V1) is a VP from the 3rd or ( - - +) octant.
- View 2 (V2) is a VP from the 4th or ( + - +) octant.
- View 3 (V3) is a VP from the 1st or ( + + +) octant.
- View 4 (V4) is a VP from the 2nd or ( - + +) octant.
|
 |
Note:
The 1st (+++) & 5th (++-) octants are used for modeling space.
The 5th (++-) octant is for objects that are below ground level.
 |
VP
V1 is a common and familiar natural viewing of an object, because
it is a viewing point as if the object were being held in your
hand. We will call this "The Normal View" to the plane. V1 is
said to be the most normal (as in normalcy) because it is the
most common familiar natural viewing of an object as experienced
by most people. "The Normal View" turns out to be extremely important,
because it is the best angle for X-ray viewing of a 3D model without
experiencing visual confusion. The parallel to the ground plane
viewing angle of normalcy for VP V1 from the ground plane is 35
degrees plus or minus 10 degrees. VPs V2 V3 and V4 are less normal
than V1, but are very good angles for X-ray viewing also. VPs
V1 V2 V3 and V4 establish a normal cruising range for viewing
a object while modeling. A person modeling tries to keep the view
as normal as possible to avoid visual trouble. The dial gauge
type diagrams at the left give a read out in degrees of angle
for user view point V1 and also show the angles of V2, V3, V4. |
| 4.7
Rotation of User View |
|
View One (V1)
|
View Two V2
|
In
the images to the left, the user view is rotated - the object
is not. The object is not moving in relationship to the World
Coordinate System. If the User Icon is not turned on, there
is no way to know if the view is being moved or the object is
being moved . The novice user who usually turns off the User
Icon, not understanding its importance, becomes confused and
lost between the movement of the View Point and the movement
of the object. |
|
View Three (V3)
|
View Four (V4)
|
The
object is rendered to avoid visual confusion. However one needs
to use the hidden lines (lines that have been hidden from view)
during the modeling process. Therefore, rendering is for visual
verification only - not to be used during the actual
modeling of the model.
Please note: The View Target 0,0,0 is
laterally moved in the images shown to the left using the pan
or the zoom window command. |
There is some normalcy in viewing
angles. However you might have noticed by now that we have only moved
the View Point VP and not the View Target VT. VT remains unchanged;
this is unnatural and strange to most people and hard to get
use to at first. You can experience and understand how strange this
is by walking around a room keeping your head and eyes on one spot
(the VT) in the middle of the room. The only way to move the VT point
is to pan or zoom to an object. However when you rotate the VP,
the VT point moves back to the origin point 0,0,0 zooming out to the
extents of the model, requiring the person modeling in 3D to zoom
in selecting with a window an area to zoom into. In a large model,
this is a very slow process for the computer to regenerate an image
of the entire model, then the window selected. A nightmare exclaims!
the person translating this text who has had no experience with CAD.
Why? someone might ask. The answer is: The indirect movement of the
VT in current CAD system interfaces is a 2D drafting legacy. The interface
is a 2D paper interface. This viewing is not so strange or unnatural
to the drafting person who works on flat two dimensional drawings.
His/her viewing angle is "normal" or 90 degrees from the surface of
the paper on which he works. The use of a paper interface by current
CAD systems for 3D modeling is irritating at best, though it
does allow the construction of large models with many objects. In
the real world, the user VT point is always moving (the turning of
your head), whereas the user View Point is more difficult to move
- you must move your body.
| 4.9
Navigation Conclusion |
The development
of a CAD interface from drafting standards is a force and fake application
of paper drafting design applied to digital design. A true digital
design interface has little or nothing to do with drafting. When a
3D model is complete, it is sometimes projected into a 2D surface
model where some drafting types of operations are applied for additions
and adjustment in order for the 2D projection to be printed on paper.
The current CAD interfaces with the paper like qualities are unlike
that of game simulation movements that provide a natural interface;
it is very easy for a user to quickly understand how to navigate in
a simulation system. A simulation game type system of navigation is
proposed as the core of Cartesian's
control system.
The pure visualization power of "Cartesian's windscreen" stemming
from the qualities of digital material has no equivalency to the visualization
capabilities of paper materials and processes. However a subjective
personal comparison can be made about interactive digital and paper
based processes. Sitting at Cartesian's helm with digital agents
at your command is much more exciting, rewarding and enjoyable than
sitting at a computer used as a substitute for pencil and paper. Trying
to fit paper processes into the digital world is not much fun. Now
sitting at a drafting board using simple tools and materials to hand
create a drawing has a calming, meditative aspect that is very enjoyable,
but it is not as efficient nor as precise as digital based design
processes.
The common starting assumption for novice users and designers of CADesign
systems is that of a "new clean sheet of paper," i.e. a blank
screen; unfortunately this is a paper legacy concept that is misleading
in the digital environment . Digital systems are based on sharing
and modifying pervious work. Unfortunately the CAD (drafting and design)
world is very slow in becoming digital because of patents and copyrights.
So, the sharing of models has not become prevalent or technically
high level. However, "reuse" was one of the basic reasons behind CADesign
systems, since they allow creation of blocks of parts, save them
and insert them into different models. It was thought that digital
based designs would be much more persistent than paper designs, because
digital data does not degrade when copied or wear out like paper.
However, digital data persistence has turned out to be a big problem
for complex reasons not covered here. The starting assumption should
always be - - to start a new model based on a previous model or parts,
that creation is the evolution of existing models. In the author's
seventeen years of consulting and installing CADesign systems,
the creation of base prototype models to create new models was the
key to any client's success. After several years of using a CADesign
system, you may come to realize that the moving, rotation and editing
of models are the most used and important modeling and design functions
in the CADesign system. However, in general, the most current
CADesign systems are designed for a "new fresh blank screen,"
because programmers who design CADesign systems do not use
them for long periods of time in production oriented environments.
What is: digital material? digital culture? and digital arts? "What
does it mean to be digital" is key to being able to successfully apply
digital arts to the design process.
| 5.1
User Coordinate System (3) |
The User Coordinate System is where creation/editing is done. It can
be viewed as a local coordinate system created for the ease of editing
objects in space. It is the space you are viewing through "Cartesian's
windscreen." In single object models, the user coordinate will be
the same as the World Coordinate System, but in large models, almost
never the same. The proper normal position for the User Coordinate
System during the creation of an entity using a "god orientation"
is the following: the X axis origin starting point is placed at the
lower left front, the positive direction of the X axis is to the lower
right front and the Y axis positive direction is down the right side
of the entity and Z is up. This is extremely important, because the
User Coordinate System position during the creation of an entity becomes
the Entity Coordinate System.
The following is
the movement of objects in relationship to the World Coordinate System.
The movement along the X, Y, and Z axis is repeated by two key commands
entered at a command line prompt. Motion studies show that using the
command line prompt with one or two keys representing the command
followed by the space bar as an enter key is the quickest form of
entry possible at the present time. However, a virtual reality interface
with the use of first person tools may represent even a faster from
of command and control for modeling systems of the future, a far more
intuitive interface.
Move Right (MR) is +X
|
Move Left (ML) is -X
|
Move Down (MD) is -Z
|
Move Forward (MF) is +Y
|
Mover Back (MB) is -Y
|
Move Up (MU) is +Z
|
Commands to move an object are the following: Move the block
to the Right (MR) moves in the positive direction of
X; Move Forward (MF) moves in the positive direction of Y;
Move Left (ML) moves in the negative X; Move Back (MB) moves
in the negative Y; Move Upward (MU) moves in
the positive Z; Move Down (MD) moves in the negative
Z. Please note that the move commands above are from the current
position and rotation of the UCS. The move command is used very often;
it is more convenient to think in right, left, forward, back, up and
down. Note the movement is based on the user's orientation or "god
orientation" not the entity's orientation or "actors orientation."
The Move Right command in the command line mode looks like this at
the user prompt:
MR in the <P>lus / Neg <X> /Y/Z axis by the EditNumber
(EN) / <9.999999999> or select:
Objects <P>revious/1/2/3...or select:
| In
CAD positive rotations are counter-clockwise around a vector
if the positive direction of the vector is pointing toward you.
In CAD a line has a start point and an end point, i.e. direction
or vector and the positive rotation around the vector follows
the conventions of the right hand rule. To help you find the
positive rotation of a line using your right hand, follow the
directions below:
*
Open your right hand
* Stick out your right thumb
* Aim your right thumb in direction of the end point of the
line
* Curl the fingers of your right hand around the line
|
 |
The direction of the curl of your right hand fingers around the line
is in the positive rotation. The uncurling of your right hand fingers
is in the negative rotation.
+ Rotation X axis (RX)
|
+ Rotation Y axis (RY)
|
+ Rotation Z axis (RZ)
|
The rotate commands by default
rotate in the positive direction or Counter Clockwise (CCW)
direction. The negative direction is a Clock Wise
(CW) direction. The Rotate command rotates
objects; it does not rotate the view or the Cartesian Coordinate System.
The rotate commands are as follows: rotate the block around the X
axis is (RX); rotate around the Y axis is (RY);
rotate around the Z axis is (RZ). Please note that the
rotate commands above are from the current UCS position. The images
above are from the WCS, but could just as easily have been from some
User Coordinate System or an entity coordinate position. The single
key command ( R)otate provides the user with rotate mode options
that become defaults for the RX, RY, RZ commands. Rotate is not used
as much as the move command. The Rotate command in the command line
mode looks like this at the user prompt:
RZ = X/Y/<Z> axis Neg/<P>lus by Entity/World/Current
<C> by <90>:
Objects <P>revious /1/2/3... or select:
| 5.5
Entity Coordinate System (4) |
The Entity Coordinate System is really an entity creation coordinate
system with a "god orientation," which is the position of the User
Coordinate System when the entity was created. The "god orientation"
being the orientation of the user / creator's right, left, forward,
back, up and down. Entity Coordinate System is not really properly
named, because it is really just the position of the User Coordinate
System given to the entity for the convenience of editing in CADesign
systems and is really just a way to move back into a convenient modeling
/ creation position. In animation systems, the entity / actor has
its own "actor orientation" system which is moved from the lower left
hand corner of the entity to the center of the actor, and the Entity
Coordinate System is rotated 180 degrees from the "god orientation"
to the "actor orientation." In animation systems, the user / director
directs the movement of an entity / "actor orientation" using the
entity / "actor orientation" rather than the "god orientation."
This feature is very convenient for animation. Animation systems
also have creation systems, in which unfortunately they continue to
use the "actor orientation" which is not easy to use for the creation
of an entity. The use of both orientations, the god for creation and
the actor for object movements in one system, turns out to work very
well. You might notice for this chapter that the move command uses
the "god orientation" to avoid confusion of mixing systems in theory.
However, in real applications the mixed use of both the god and actor
orientations is quite natural and actually avoids confusion. Depending
on the CAD system chosen, you may or may not have access to the Entity
Coordinate System. Most people are not aware of this system or its
different orientations. However it is a very powerful system and will
be one of the core systems necessary for Cartesian's navigation
and visualization systems.
 |
Alice
(http://www.alice/org) is a 3D Interactive Graphics
Programming Environment for Windows 95/98/NT built by the
Stage 3 Research Group at Carnegie Mellon University. The
Alice project is a public service to the wider computing and
artistic communities. The current version of Alice authoring
tool is free to everyone and runs on computers that are commonly
available for reasonable prices. Worlds created in Alice
can be viewed and interacted with inside of a standard web
browser once the Alice plug-in has been installed. Alice
is primarily a scripting and prototyping environment for 3D
object behavior, not a 3D modeler; this makes Alice
much more like LOGO (http://el.media.mit.edu/logo-foundation/logo/turtle.html)
than AutoCAD. By writing simple scripts, Alice users
can control object appearance and behavior, and while the
scripts are executing, objects respond to user input via mouse
and keyboard.
You
can create 3D models using a web browser with Teddy2.
Alice runs Teddy2, a sketched based 3D modeling tool developed
by Takeo Igarashi at the University of Tokyo. During
the creation process, the "god orientation" is used. However,
at the end of the process when you save the model, Teddy2
has you orient the front of the object to face you.
Saving the model in that position gives the object the "actor
orientation" shown in the image at the left. So objects
in Alice have their own sense of direction. This makes the
control of the object very easy. Try loading Alice and using
their tutorial to create a 3D object by sketching.
|
| 5.6
Group Coordinate System (5) |
Every group
or block of objects has an insert point or base point assigned to
it by which to insert, move or rotate it as a group. This coordinate
system is an essential system. Without this system, one can not
insert a model or part of a model into the model being worked on.
It is the system that turns all of the rest of the models into a
library of parts or blocks that can be used repeatedly. It is a
digital extension of yourself that you can share digitally with
others and giving you value in the digital world. Digital modeling
is part of the growing landscape of digital containing digital swarms
of information ... to be used from any location on the Net.
Knowledge provided
in this CAD chapter is a summery of twenty years of experience in
computer aided design. Much of the information contained here is not
found in any other educational texts of which I am aware. The goal
of this chapter is to transfer the knowledge needed to set up a digital
framework for doing the exercises below and teaching yourself a CAD
system of your choice. It would be a waste of my time and yours to
present knowledge, information, and exercises that are common place
and can be found on the WWW easily. Instead I urge you to access that
easily found information yourself using the WWW. Learning the line,
circle command in one particular CAD system is best done by yourself
using that particular system's online help and tutorial. What is missing
from the online help systems is why and how to apply digital systems
to 3D design. I have found only one such book, AutoCAD 3D Design
and Presentation, M. Bousquet and J. Hester, New Riders Publishing,
Carmel, Indiana, USA (1991) ISBN 0-934035-81-4. Though it does not
have an educational focus or an overall approach, it does give step
by step procedures for AutoCAD as a 3D design system. Follow the exercises
below and you will be well on your way to CAD mastery.
Exercise 1
- Take out a piece of paper and pencil.
- On one half of a sheet of paper, draw the Cartesian Coordinate
System's X, Y, Z axis from the - - + view (V1).
- Divide the axis in the positive direction into 10 equal segment
starting from the origin point.
- Label the drawing with the first principle of Cartesian existence.
Exercise 2
- Using the axis drawing from Exercise 1 - construct a 4,5,6 unit
size box on the axis starting at 0,0 * Tip: Graph out the
following points on the axis drawing and then connect the lines:
0,0,0 4,0,0 4,5,0 0,5,0
0,0,6 4,0,6 4,5,6 0,5,6
- Label the eight corners of the 4,5,6 box
- Relative from point 4,5,6 - place a point at 4,4,4
Exercise 3
- Install a CADesign program of your choice on a system
of your choice.
- Create a 3D model of the paper drawing done in Exercises 1 and
2.
- Reflect on and evaluate the CADesign software program.
Exercise 4
- Load Alice and use Teddy 2 to sketch a soft object / toy.
http://www.alice.org/
- Load FreeCAD - use the tutorial and evaluate the addition of
reverse kinematics to CAD. http://www.askoh.com/
- Load HyperFun - use the HyperFun tutorial and evaluate the concept
of F-rep. http://www.hyperfun.org/
Exercise 5
- Get a package of Lego blocks and calipers with LED read out
and make precise 3D models of them with a CADesign of your choice.
The web site http://GNUCAD.org will
have an extended list of exercises / links missing from this paper.
|
|
