RenderMan Procedural Primitives
Randomness


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Introduction

Being able to generate points distributed randomly within or over a surface can be useful when modeling phenomena such as fireworks. This tutorial presents in listings 1 to 9 some useful utility procs implemented in Python, Tcl and the 'C' programming language. The implementations of the utility procs will be given followed by examples of their use.


Proc randBetween

This proc returns a random value between two input values. Although it is a very simple it is surprisingly useful for positioning objects, such as RenderMan points and curves, as well as setting randomized rgb components of colors.


Listing 1 - Python Implementation

import random
  
def randBetween(min, max):
    return random.random() * (max - min) + min

Listing 2 - Tcl Implementation

proc randBetween { min max } {
    return [expr rand() * ($max - $min) + $min]
    }

Listing 3 - 'C' Implementation

#include <stdlib.h>
  
double randBetween(double min, double max)
{
return ((double)rand()/RAND_MAX) * (max - min) + min;
}

Procs length & normalize

The proc length returns the length of a vector. The proc normalize normalizes a vector. Typically, the input values to this proc are the xyz position of a geometric point. However, the location of the geometric point can be considered to represent the "head" of a vector and as such it can be converted to a unit vector.


Listing 4 - Python Implementation

import math
  
def length(x, y, z):
    return math.sqrt(x*x + y*y + z*z)
  
def normalize(x, y, z):
    len = length(x, y, z)
    return x/len, y/len, z/len

Listing 5 - Tcl Implementation

proc length { x y z } {
    return [expr sqrt($x*$x + $y*$y + $z*$z)]
    }
  
proc normalize { x y z } {
    set len [length $x $y $z]
    return [list [expr $x/$len] [expr $y/$len] [expr $z/$len]]
    }

Listing 6 - 'C' Implementation

#include <stdlib.h>
#include <math.h>
  
double length(double pnt[3])
{
return sqrt((pnt[0] * pnt[0]) + 
            (pnt[1] * pnt[1]) + 
            (pnt[2] * pnt[2]));
}
  
void normalize(double pnt[3])
{
double len = length(pnt);
pnt[0] /= len;
pnt[1] /= len;
pnt[2] /= len;
}

Proc scaleVector

This proc returns the xyz values of a vector re-sized to a specified length.


Listing 7 - Python Implementation

def scaleVector(x, y, z, sc):
    return x*sc, y*sc, z*sc

Listing 8 - Tcl Implementation

proc scaleVector { vect sc } {
    set X [expr [lindex $vect 0] * $sc]
    set Y [expr [lindex $vect 1] * $sc]
    set Z [expr [lindex $vect 2] * $sc]
    return [list $X $Y $Z]
    }

Listing 9 - 'C' Implementation

void scaleVector(double pnt[3], double sc)
{
pnt[0] *= sc;
pnt[1] *= sc;
pnt[2] *= sc;
}

Examples of Use

This section provides some simple examples of how the procs given in listing 1 to 9 can be used with RenderMan's point primitive. For brevity, the examples are only given in Python.


RiPoints in a Rectangular Volume


Figure 1


Listing 10 - rectangular box

import sys, math, random

def box(width, height, depth, num, size):
    print 'Points \"P\" ['
    for n in range(num):
        x = randBetween(-width/2, width/2)
        y = randBetween(-height/2, height/2)
        z = randBetween(-depth/2, depth/2)
        print '%s %s %s' % (x, y, z)
    print '] \"constantwidth\" [%s]' % size
    print '\"Cs\" ['
    for n in range(num):
        r = randBetween(0, 1)
        g = randBetween(0, 1)
        b = randBetween(0, 1)
        print '%s %s %s' % (r, g, b)
    print ']'
  
def main():
    args = sys.stdin.readline()
    while args:
        arg = args.split()
        pixels = float(arg[0])
        width = float(arg[1])
        height = float(arg[2])
        depth = float(arg[3])
        num = int(arg[4])
        size = float(arg[5])
  
        print 'TransformBegin'
        box(width, height, depth, num, size)    
        print 'TransformEnd'
        sys.stdout.write('\377')
        sys.stdout.flush()
        # read the next set of inputs
        args = sys.stdin.readline()
  
if __name__ == "__main__":
    main()

RiPoints in a Ring


Figure 2


Listing 11 - Ring

import sys, math, random

def ring(rad, num, size):
    print 'Points \"P\" ['
    for n in range(num):
        x = randBetween(-1, 1)
        y = 0
        z = randBetween(-1, 1)
        x,y,z = normalize(x,y,z)
        x,y,z = scaleVector(x,y,z,rad)
        print '%s %s %s' % (x, y, z)
    print '] \"constantwidth\" [%s]' % size
    print '\"Cs\" ['
    for n in range(num):
        r = randBetween(0, 1)
        g = randBetween(0, 1)
        b = randBetween(0, 1)
        print '%s %s %s' % (r, g, b)
    print ']'
  
def main():
    args = sys.stdin.readline()
    while args:
        arg = args.split()
        pixels = float(arg[0])
        rad = float(arg[1])
        num = int(arg[2])
        size = float(arg[3])
  
        print 'TransformBegin'
        ring(rad, num, size)    
        print 'TransformEnd'
        sys.stdout.write('\377')
        sys.stdout.flush()
        # read the next set of inputs
        args = sys.stdin.readline()
  
if __name__ == "__main__":
    main()

RiPoints on a Disk


Figure 3


Listing 12 - Disk

import sys, math, random

def disk(rad, num, size):
    print 'Points \"P\" ['
    for n in range(num):
        x = randBetween(-1, 1)
        y = 0
        z = randBetween(-1, 1)
        x,y,z = normalize(x,y,z)
        randRadius = randBetween(0, rad)
        x,y,z = scaleVector(x,y,z,randRadius)
        print '%s %s %s' % (x, y, z)
    print '] \"constantwidth\" [%s]' % size
    print '\"Cs\" ['
    for n in range(num):
        r = randBetween(0, 1)
        g = randBetween(0, 1)
        b = randBetween(0, 1)
        print '%s %s %s' % (r, g, b)
    print ']'
  
def main():
    args = sys.stdin.readline()
    while args:
        arg = args.split()
        pixels = float(arg[0])
        rad = float(arg[1])
        num = int(arg[2])
        size = float(arg[3])
  
        print 'TransformBegin'
        disk(rad, num, size)    
        print 'TransformEnd'
        sys.stdout.write('\377')
        sys.stdout.flush()
        # read the next set of inputs
        args = sys.stdin.readline()
  
if __name__ == "__main__":
    main()

RiPoints on a Cone


Figure 4


Listing 13 - Cone

import sys, math, random

def cone(rad, num, size):
    print 'Points \"P\" ['
    for n in range(num):
        x = randBetween(-1, 1)
        y = 0
        z = randBetween(-1, 1)
        x,y,z = normalize(x,y,z)
        randRadius = randBetween(0, rad)
        x,y,z = scaleVector(x,y,z,randRadius)
        y += 1 - randRadius # <<---
        print '%s %s %s' % (x, y, z)
    print '] \"constantwidth\" [%s]' % size
    print '\"Cs\" ['
    for n in range(num):
        r = randBetween(0, 1)
        g = randBetween(0, 1)
        b = randBetween(0, 1)
        print '%s %s %s' % (r, g, b)
    print ']'
  
def main():
    args = sys.stdin.readline()
    while args:
        arg = args.split()
        pixels = float(arg[0])
        rad = float(arg[1])
        num = int(arg[2])
        size = float(arg[3])
  
        print 'TransformBegin'
        cone(rad, num, size)    
        print 'TransformEnd'
        sys.stdout.write('\377')
        sys.stdout.flush()
        # read the next set of inputs
        args = sys.stdin.readline()
  
if __name__ == "__main__":
    main()

RiPoints on a Cylinder


Figure 4


Listing 14 - Cylinder

import sys, math, random

def cylinder(rad, depth, height, num, size):
    print 'Points \"P\" ['
    for n in range(num):
        x = randBetween(-1, 1)
        y = 0
        z = randBetween(-1, 1)
        x,y,z = normalize(x,y,z)
        y = randBetween(depth, height) # <<---
        print '%s %s %s' % (x, y, z)
    print '] \"constantwidth\" [%s]' % size
    print '\"Cs\" ['
    for n in range(num):
        r = randBetween(0, 1)
        g = randBetween(0, 1)
        b = randBetween(0, 1)
        print '%s %s %s' % (r, g, b)
    print ']'
  
def main():
    args = sys.stdin.readline()
    while args:
        arg = args.split()
        pixels = float(arg[0])
        rad = float(arg[1])
        depth = float(arg[2])
        height = float(arg[3])
        num = int(arg[4])
        size = float(arg[5])
  
        print 'TransformBegin'
        cylinder(rad, depth, height, num, size)    
        print 'TransformEnd'
        sys.stdout.write('\377')
        sys.stdout.flush()
        # read the next set of inputs
        args = sys.stdin.readline()
  
if __name__ == "__main__":
    main()

Spheres on a Sphere


Figure 5


Listing 15 - Sphere

import sys, math, random

def spheres(rad, num, size):
    for n in range(num):
        x = randBetween(-1.0, 1.0)
        y = randBetween(-1.0, 1.0)
        z = randBetween(-1.0, 1.0)
        x,y,z = normalize(x,y,z)
        print 'TransformBegin'
        print 'Translate %s %s %s' % (x, y, z)
        print 'Color %s %s %s' % (x, y, z)
        print 'Sphere %s %s %s 360' % (size, -size, size)
        print 'TransformEnd'
    
def main():
    args = sys.stdin.readline()
    while args:
        arg = args.split()
        pixels = float(arg[0])
        rad = float(arg[1])
        num = int(arg[2])
        size = float(arg[3])
  
        print 'TransformBegin'
        spheres(rad, num, size)    
        print 'TransformEnd'
        sys.stdout.write('\377')
        sys.stdout.flush()
        # read the next set of inputs
        args = sys.stdin.readline()
  
if __name__ == "__main__":
    main()


© 2002- Malcolm Kesson. All rights reserved.