|Column Tag:||Tools of the Trade
MacWireFrame & Desktop Lawyer
By Dave Kelly, MacTutor Editorial Board
MACWIREFRAME 3-D Graphics
Amplified Intelligence has recently released their three-dimensional graphics library for THINK Pascal. The MPW Pascal counterpart has been available for some time now. The package includes a sample application program, MacWireFrame that illustrates the capabilities of the 3-D library.
MacWireFrame is a wire-frame editor used to create three-dimensional wire-frames. A wire-frame is a mathematical term used to describe a three-dimensional object formed by lines or wires. The wire-frame lines or wires represent the path between two vertices.
The source code supports five key data types. By understanding these data types, you will be ready to use the MacWireFrame library.
MacWireFrame uses linked arrays to represent rotation and scaling matrices, translation vectors, three dimensional points and lines in space, two dimensional points and lines in planes and view matrices used to transform three dimensional data into two dimensional data. These linked arrays are dynamically allocated array elements that consist of a handle to a record containing a real number and handles to two other linked array elements (the next row element and the next column element). MacWireFrame performs matrix multiplication on linked arrays to accomplish rotation, scaling and mapping from three down to two dimensions.
A spacepoint is an array of three real numbers: the X, Y, and Z coordinates of a point in space. A spacepoint is the basic building block of wireframes. The MacWireFrame manual explains the spacepoint type in an amusing way:
SpacePoint = array[1 3] of REAL;
The single line of code above really says a lot about our universe. It says that a point in space is defined by three real numbers.
Once, back a long time ago, I was walking into the cafeteria in high school when I noticed that the nerd crowd was having a heated argument and, being a troublemaker, I went over to start trouble. I quickly learned that they were arguing about whether it is possible to assign a real number to every point in space.
Why not ask my smart friend, Dave, I thought. Dave was one of my high school buddies who later went on to get a Ph.D. in Physics and became a physics professor. I began to explain the problem to Dave: Say that you started out with one line in space and started assigning numbers to it. By the time you were done, you would have used up all the real numbers and wouldnt have any left over for any of the other points in space. Yes, my friend Dave answered, but what if, instead of a straight line, you used a single squiggle line that went around all over the place until it eventually hit every point in the universe?
This same type of problem has vexed mathematical thinkers since the beginning of Man. In fact, according to legend, there was once a cave man named Grunt, who lived back in the days when math was a lot more simple. People back then would count by saying, one, two, three, many.
For example, Grunt had two wives and many children. On one of his recent hunting trips, Grunt had killed two deer, one antelope and many jack rabbits. Back then, numbers above two to the second power were so rare that, for most practical purposes, it didnt make any difference just exactly how big they were -- kind of like numbers larger than two to the thirty second power are today.
But then one day Grunt began to think about mathematics. Near Grunts cave were two piles of rocks, and although each pile had many rocks, Grunt began to wonder which pile had more rocks. Grunt wished that he could first count the number of rocks in one pile and then count the rocks in the second pile, so that he could find out which pile had more rocks, but he lacked the mathematical sophistication to do this.
For awhile, Grunt and his friends sat around arguing about which pile of many rocks actually contained more rocks than the other, until finally Grunt came up with an idea. Grunt thought, What if I take one rock off the first pile of many rocks and then one rock off the second pile of many rocks and keep doing this until finally one of the piles has all its rocks used up. Then at last, I will know which pile has more rocks. Grunt had discovered the mathematical concept of a one to one correspondence.
Of course, each pile of many rocks had many rocks in it and Grunt soon got tired and hungry and went off to pick berries before he ever really found the answer to his question, but never the less Grunt had had a brilliant idea.
The first line of code in the MacWireFrame Editor uses only slightly more complicated thinking. A Mac II computer with its thirty two bit registers can only comprehend numbers up to two to the thirty second power. There are a lot more points than that in the universe and a lot more points than that in the theory used by the MacWireFrame Editor.
There are more points in the universe than there are real numbers. This might be hard for us to understand today because infinity is somewhat more of a difficult concept today than it was in Grunts day. Infinity really means so many that it is theoretically impossible to count.
What the first line of code in the Editor says to the computer is that there is a one to one correspondence between every point in the universe and every possible ordered triplet of real numbers.
A vertex is a three-dimensional point in space that is connected to three other vertices by lines or wires. It is one of the key building blocks of a wire-frame. A vertex consists of a spacepoint and an array of handles to three other vertices. A wireframe is then built from an interconnected set of vertices. Representing wireframes as interconnected vertices has numerous advantages. The most spectacular of these advantages can be seen while doing three dimensional dragging. If you select some of the vertices in a wireframe and drag them while leaving the others behind, the connections between the selected and unselected vertices will stretch like rubber bands.
Another advantage is that since vertices are linked with handles to other vertices, operations need to be performed only once instead of three times. This is because when drawing a vertex alone, you would draw the three lines that connect to it. Since the vertices are linked to each other, it is not necessary to draw the lines twice. This makes the operation much more efficient.
Some surface models based on polygons claim to have wireframe capabilities, but each line in a wireframe is associated with at least two polygons in a surface model so the same operation done to an interconnected set of polygons takes six times as long as in MacWireFrame.
A pointlist is a linked list of vertices. This type comes in handy for performing operations on vertices because of its linear nature. Vertices have three ways to go from any given vertex, but on a pointlist, there is only one.
An entity contains all information needed by MacWireFrame to maintain the display interface. There are five windows available in MacWireFrame: isometric, top, front, side and custom views. An entity maintains the relationship of these views. In addition, an entity type contains a field that keeps track of which vertices are highlighted.
A space point is a field in the type vertex which is a field in the type pointlist which is a field in the type entity. Thus an entity represents all of the space points and vertices in an object. The wireframe entity shown in the figure is made up of two cube objects. The smaller one was scaled copied and pasted on top of the larger one using the MacWireFrame editor.
Both ends of a wire-frame wire or line is tied to a vertex. The wires are straight (no curves) and have no hidden lines. Thus, you can see that every vertex has three lines attached to it and all of the lines and vertices make up the entire entity.
The MacWireFrame application allows you to create wire-frames based on a cube or a tetrahedron. From there, you can add or remove lines, rotate the object, rotate the vertex, scale the object, scale a portion of the object, translate an object or drag the object with the mouse. A dimension dialog can be used to tell you the distance between two highlighted vertices of an object. TransformObject is the function at the heart of MacWireFrame that makes things tick. You give the TransformObject function a pointlist and a predefined linked array. The function looks at the size and if it is a translation vector then it will add the vectors to each point on the list thus implementing translation. If the matrix is a 3X3 matrix, then TransformObject will matrix multiply each spacepoint on the pointlist thus implementing rotation and scaling.
The source code in THINK Pascal format is fully documented in a 78 page spiral bound book. Between the comments in the source code and the manual an experienced programmer should have no problem understanding how MacWireFrame is put together. However, some of the routines may require some understanding of matrix mathematics. It isnt necessary to have a full understanding of all of the math though. The manual illustrates this with the following story:
Recently I picked up an article in a magazine which used the phrase, matrix multiplication is well understood, and maybe this is the case if youre a Ph.D. physicist like my friend Dave, but most people like my punk rocker friend Dusty dont really understand it too well.
Punk rockers in Sacramento have this drinking game called quarters. What you do is take a glass and put it in the middle of the table. Everyone sits around the table. Going around in a circle each player tries to bounce the quarter off the table and up into the glass. If you make it you get to pick one of the other players and they have to drink. If you miss, its the next players turn unless you want to chance it, but if you miss then you have to drink.
There is one other rule in the punk rock Sacramento version of quarters. If you get really lucky and make it three times in a row you get to make up a new rule. One time Dusty made up a this rule that before you drink you have to grab your left ear with your right hand and yank it three times and as you yank it say arf, arf, arf. But if you forget to do this you have to drink again. Since the winner of the game is the one left standing when everyone else has passed out, and as the game progresses people get more and more likely to forget the rules, this can be really strategic.
Once I tried to explain matrix multiplication to Dusty, how you first multiply this row by this column and so on. But, why do you do it that way? Why not multiply that row and this column?, Dusty asked. I explained to Dusty its just a rule that somebody made up that proved to be useful. Oh, I get it, this is some rule that some old 19th century mathematician made up., Dusty said. Making up strange rules was something that for Dusty was well understood.
Too bad Dusty hadnt lived in the 19th century or he could have been a great mathematician. On the other hand its kind of sad that Sir William Rowan Hamilton didnt live in our time. While matrix multiplication would have already have been thought of, he probably would have been great at the game of quarters.
You can see from these stories that the manual tries to make the subject of wireframes interesting, not just dry technical reading. The first half of the book tells users how to make use of the MacWireFrame application. The last half describes the UNIT modules used and each procedure and function is described. Youll need to become familiar with each function and procedure if you intend to use the MacWireFrame source code to create your own customized wireframe application.
Each UNIT module is described first with an overall description, then with a description of routines. Next all of the variables used. The only improvement that could be made here would be to describe the function of each variable in more detail. Also, there is no index to the manual. Since each module is described, it is easy to get familiar with all of MacWireFrames procedures and functions.
Amplified Intelligence is now offering a special price of $299 if you order through MacTutor. Any of you that are interested in 3D graphics will find MacWireFrame useful.
MacWireFrame is available from:
2810 Redding Ave.
P. O. Box 189279
Sacramento, CA. 95818
Price: $299 for a limited time only; List Price: $495
Requires: Macintosh II family computer with Color Monitor, THINK Pascal 2.0 or later.
Programming ability is not required for use of the MacWireFrame Application. Programming will be required for use of the source code. Understanding of matrix math is helpful.
Not copy protected.
THE DESKTOP LAWYER
Lawyers are generally disliked. Most of you have seen Nolo Presss books on various Do-It-Yourself law topics. Nolos WillMaker lets you fill in the blanks to complete your will in just a few minutes. The Desktop Lawyer has this same Do-It-Yourself law attitude. Its produced by The Open University and distributed by National Media Associates.
In the Desktop Lawyer is not an application, but is a set of over 300 legal documents in MS Word format. (The templates are available on MS/DOS disks for WordPerfect and in ASCII files). Each template is a complete legal document that can be customized to suit your needs. Laurence J. Pino, ESQ of the law firm of Pino & Dicks of Orlando, Florida, produced the templates to simplify Do-It-Yourself law.
Developers will be especially interested in several of the templates including:
Joint Venture Agreement
Business Consultant Agreement
Employee Confidentiality , nondisclosure and nonuse agreement
Sales Representative Agreement (Company)
Independent Contractor Agreement
Computer Hardware and Software Marketing Agreement
Product License Agreement
Grant of right to use name
Contract for Sale and Purchase of Business
Master Equipment Lease
Third Party Rental Agreement
Articles of Incorporation
Contract for sale of personal property
The other templates include Business Sales and Closing, Investment, Real Estate, Estate Planning, Mortgages, Wills, trusts, Collection documents, agreements, leases, rentals, and construction. The 137 page manual includes information on where to file documents and filing fees. In addition, there are tips and comments for each of the documents types.
Although the templates are only available in MS Word format, you will find that they are not difficult to customize. A new version of the Desktop Lawyer is being released in September 1991 with a revised manual that includes instructions for each legal document. The new manual will include information such as how to fill in each form, the circumstances you do and dont need an attorney, and where to find basics and procedures in other parts of the manual for making the transaction legal. Four new forms are also being added.
There is really no other package with as many law forms in one package. People that have used the Desktop Lawyer have said that they have saved several times the cost of the material. It has something for every business owner.
The Desktop Lawyer is distributed by:
U. S. Software Resource of
Novato, CA. and Houston, TX.
8 Digital Drive, Suite 100
Novato, CA. 94949
Special Introductory price $99.95 (till Dec. 31st, 1991)
The Desktop Lawyer is published by:
The Legal Institute of America for
The Open University
P. O. Box 1511
Orlando, Florida 32802
Not copy protected.