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-
-
- I would ike to warn the reader right now that I am a very poor programer, I
- am sure that there are much easier and faster ways to achieve the objectives
- of this program than the way I have done it. I learned to program in basic
- as I was writing this program. The program itself was written in qbasic which
- came with my version of Ms-Dos 5.00. I had to rely heavily on sequential files
- to get this program to work because of the 128k enviorment limit on my version
- of qbasic.
-
- I will assume that the reader of this document is famillar with
- l-systems in my explaniation of the inner workings of the program. I will
- begin with the 'turtle' interpitation.
-
- The sub called turtle handles the drawing of the l-system. It
- responds to the following commands. The program keeps track of the
- turtles position in 3-space and also keeps track of the three vectors
- H, L , and U. which represent the turtles heading, the direction to the
- Left of the turtle, and the direction up from the turtle respectivly. The
- turtle responds to the following commands:
-
- F(x) : move forward and draw a line x units in the direction of H
-
- f(x) : move forward without drawing a line x units in the direction
- of H
-
- +(x) : rotate the turtle by x (in radians) about the U vector.
- x can be positive or negative depending on the direction
- wanted.
-
- &(x) : rotate the turtle by x (in radians) about the L vector.
- x can be positive or negative.
-
- /(x) : rotate the turtle by x (in radians) about the H vector.
- x can be positive or negative.
-
-
-
- [ : stack the current position of the turtle along with the
- orientation of the turtle. Also stacks current color, line
- length, line width, and just about everything else that
- effects the drawing of the object.
-
- ] : pull from the stack and make current the orientation, position,
- color, width, length, and everything else that effects the
- drawing of the object.
-
- !(x): change the width of the lines be drawn to x.
-
- $ : roll the turtle so that the L vector fufills the following
- equation:
- V X H
- L = -------
- |V X H|
-
- then recalulate U so that U = H X L
-
- V is the vector pointing opposite to that of gravity.
-
-
- --------------------------------------------------------------------
-
- The turtle orientation is also effected by a tropisim vector T.
- After every line segment is drawn with F(x) the H vector is rotated
- slightly in the direction of T.
-
- This rotates the turtle about the vector H X T. the angle of
- rotation is determined by getting the angle alpha between H and T
- and then rotating the turtle e*alpha degrees. e is a constant
- that represents how much T effects the turtle.
-
- -----------------------------------------------------------------------
-
- < text > : transfer control to the polygon generator and pass the
- text within the brackets to the polygon generator.
- when the polygon generator is finished executing
- the commands stored in the text it restores the
- turtle information as it was before the call.
-
- the polygon generator responds to the following commands
-
- { : push the current polygon onto the top of the
- polygon stack and start a new polygon.
- * : append the new vertex to the current polygon
- the coordienits of which are determined by the
- current position of the turtle.
- } : Draw the current polygon using the supplied
- vertices, then pop the top polygon from the
- polygon stack.
- F(x): Move forward x units and use the result
- as the next vetex
- G(x): Move forward, do not create new vertex
-
-
- This is not yet completly implemented....
-
- ______________________________________________________________________
-
- Everything else in the file being read is ignored.
-
-
- I assume that the reader is famillar with the way that the productions
- work in l-systems. In this program it is handled by a sub called
- 'productions'. This does the replacements of the symbols [,],{,},and G
- along with a few other commands that do not have parameters assioated with
- them. When it comes to a word that has parameters then it passes control
- to the sub 'handler' which then passes control to the appropriate sub
- that replaces it according to the rules within that sub.
-
- for example if the program hit A(1,10) then it would pass control
- to the sub 'handler' which would in turn pass control to the sub A.
- look at sub A to see how the production works.
-
- I had to write my own subs that converted between numeric and string type
- variables for the parameters since the way qbasics built in conversion
- routines occasionaly produced strings that had charicters that the program
- uses to seperate the numbers. For example, if I used the built in numeric
- to string conversion it would sometimes produce a string that had a comma
- or ) symbol both of which would cause the getparam sub to think that it
- was done reading the number in the case of a comma or done reading the
- parameters in the case of ). I could remedy this problem by using
- a random access file type but qbasics online help wasn't very helpful
- in describing the proper use of fields in conjunction with a random access
- file.
-
-
- Heres a list of the subs and what they do:
-
- poly : not currently being used
- polygon : reads the file 'points.raw' that is produced
- by the branchman sub, anb creates a raw triangle
- file for programs such as raw2pov
- This sub usually produces output that works
- fine with raw2pov. Unfortunatly when the file
- size gets large raw2pov aborts with the error
- 'unexpected end of file' on the last line number
- of the file generated. I have not found a reason for
- this.
-
- branchman : This sub is called from the turtle sub after every
- F(x) command. It stack the H and L vectors
- and creates points on a octogon by rotating L
- around H 45 degrees 8 times and recording the
- values in 'points.raw'.
-
- tropisim : This sub is called after every F(x). This has
- alredy been explained above. If you do not want
- this effect on the object make T()=0
-
- stack(stype$): this sub controls the stacking operation
- for the [ and ] commands. the array stac()
- is the stack it controls.
-
- rotateX: does the rotation for the $ command.
- widthman: This sub is called from the turtle sub
- when the !(x) command is encountered. sets the variable
- wid to x. wid is used by branchman as a scalar
- against L to control the width of the branches.
-
- rotateU: rotates the turtle about the U vector.
- rotateL: rotates the turtle about the L vector.
- rotateH: rotates the turtle about the H vector.
-
- trans3d2d: translates the 3d co-ords to 2d co-ords for viewing
- while turtle draws the initial shape.
-
- drawline: draws a line between the old location of the
- turtle to the new location. called by movef.
-
- movef : called by turtle when F(x) or f(x) is encountered
- in the file being read. If F(x) was passed then
- drawline is called. if f(x) then drawline is not called
-
- number2string(anumber) : converts anumber to number$
-
-
- getparams : called by a production sub. returns all of the
- parameters in the way of an array called numberarray.
- the first valuse in numberarray is the number of
- parameters in the word being looked at.
- ie if A(10,1) were encountered by the productions
- sub control would be passed to the sub A which
- would in turn call getparams to get the
- parameters assioated with A. getparams would then
- return numberarray which would look like:
- numberarray(1,1) = 2 ; since there are
- 2 pararmeters
- numberarray(1,2) = 10 ; value of
- first parameter
-
- numberarray(1,2) = 1 ; value of 2nd parameter
-
- this sub also calls string2num to convert the
- string format to a numeric variable.
-
- string2num: (ntemp$) converts ntemp$ to a numeric variable
- atemp.
-
- productions: reads the file Axiom and produces a file
- called 'commands.raw' for use by the turtle
- sub.
-
- convst: used by num2string
-
- handler : used by productions to sort out what it is doing and
- and where to pass control to.
-
- f : production sub for the command F(x)
- sf : production sub for the command f(x)
- A : production sub for the command A(x,y)
- B : production sub for the command B(x,y)
- cC: production sub for the command C(x,y)
- D : production sub for the command D(x1,x2,...,xn)
- RU: production sub for one of the rotate commands
- RL :' '
- RH : ' '
- decr: production sub for the !(x) command
- colour: not yet implemented, but will be a production sub
- for '(x) where x is the new color to draw in.
-
- powercon : used by string2num
-
-
-
- initial variables:
- scale : the scale at which the
- shape is drawn on the screen
- _ _ _ _
- V(1)-V(3): V = V(1)i + V(2)j + V(3)k
- h(1)-h(3): the inital heading vector H
- _ _ _ _
- H = h(1)i + h(2)j + h(3)k
-
- l(1)-l(3): same as above but for the L vector
- u(1)-u(3): same as above but for the u vector
- phi: the viewing angle for the shape as it is
- drawn on string from the positive z-axis
-
- th: the viewing angle measured from the x-axis
- a0 : branching angle from trunk
- a2 : branching angle from lateral axes
- r1 : contraction ratio for the trunk
- r2 : contraction ratio for the branches
- ds : divergence angle
- wr : width decrease rate
- e : the effect of T on the turtle (tropisim)
- T(1)-T(3): the T vector for tropisim calculations
- _ _ _ _
- T = T(1)i+T(2)j+T(3)k
-
-
-
- I almost forgot. This program uses axes orientated in the
- following way :
- |z
- | /
- | /
- | /
- --------------+--------------
- / | y
- / |
- / x |
- |
-
- I hope that this poor description helps whomever is reading this.
-
- If you make any changes that speed this program up or add new functions
- I would be interested in seeing the code. You can contact me via The Graphics
- Alternative BBS as Ed Smith.
-
- P.S. I guess I am placing this code in the public domain. Use it
- as you see fit. I got most of my ideas for the program for a book
- called 'The Algorithmic Beauty of plants.' It's a good one.
-
-
-
-
-
- Ed Storm
- (209)474-9159
- May 11, 1993
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