# Point Distributions

📅 2010-Sep-14 ⬩ ✍️ Ashwin Nanjappa ⬩ 🏷️ distributions, geometry ⬩ 📚 Archive

A variety of point distributions are used in computer graphics and computational geometry to test out algorithms. Below are a few common point distributions and code to generate points in 3D. Assume that `random()` is a random function that returns a floating point value in the range (0.0-1.0).

Uniform Distribution

Uniform distribution is the most common distribution used in practice. Generate point using random values of x, y and z.

``````x = random();
y = random();
z = random();``````

Sphere Distribution

``````do {
x = random() - 0.5;
y = random() - 0.5;
z = random() - 0.5;

d = ( x * x ) + ( y * y ) + ( z * z );

} while ( ( d < ( 0.45 * 0.45 ) || ( d > ( 0.5 * 0.5) ) ) );``````

Half Sphere Distribution

``````do {
x = random() - 0.5;
y = random() - 0.5;
z = random() - 0.5;

d = ( x * x ) + ( y * y ) + ( z * z );

} while ( ( z >= 0.2 ) || ( d < ( 0.45 * 0.45 ) ) || ( d > ( 0.5 * 0.5) ) );``````

Ball Distribution

``````do {
x = random() - 0.5;
y = random() - 0.5;
z = random() - 0.5;

d = ( x * x ) + ( y * y ) + ( z * z );

} while ( d > ( 0.49 * 0.49 ) );``````

Empty Ball Distribution

``````do {
x = random() - 0.5;
y = random() - 0.5;
z = random() - 0.5;

d = ( x * x ) + ( y * y ) + ( z * z );

} while ( d < ( 0.45 * 0.45 ) );``````

Ellipsoid Distribution Ellipsoid has a surface but no volume inside.

``````a = 0.5;
b = 0.5;
c = 0.2;

do {
x = random() - 0.5;
y = random() - 0.5;
z = random() - 0.5;

d = ( ( x * x ) / ( a * a ) ) + ( ( y * y ) / ( b * b ) ) + ( ( z * z ) / ( c * c ) );

} while ( ( d <= 1.4 ) || ( d >= 1.5 ) );``````

Pancake Distribution

``````a = 0.5;