02 Drawing shapes with math

Polar coordinates: distance and angle

length gives the distance, atan the angle. Petals and spirals come from these two.

Petals5

112

Petal depth0.08

00.15

Twist0.00

-88

ExerciseTune values0%

Make a three-petal flower

Runs once per pixelDrag numbers, or edit the code

void main() {
  vec2 p = (gl_FragCoord.xy - 0.5 * uResolution) / min(uResolution.x, uResolution.y);
  float r = length(p);
  float a = atan(p.y, p.x);          // -pi .. pi
  a += r * 0.000;                // further out turns more -> spiral
  float edge = 0.28 + 0.080 * cos(a * 5.000);
  float mask = 1.0 - smoothstep(edge, edge + 0.006, r);
  float turn = fract(a / 6.283185 + 0.5);   // angle -> 0..1
  vec3 ink = mix(vec3(0.96, 0.43, 0.30), vec3(0.48, 0.83, 0.69), turn);
  vec3 color = mix(vec3(0.06, 0.10, 0.14), ink, mask);
  gl_FragColor = vec4(color, 1.0);
}

void main() {
  vec2 p = (gl_FragCoord.xy - 0.5 * uResolution) / min(uResolution.x, uResolution.y);
  float r = length(p);
  float a = atan(p.y, p.x);          // -pi .. pi
  a += r * 0.000;                // further out turns more -> spiral
  float edge = 0.28 + 0.080 * cos(a * 5.000);
  float mask = 1.0 - smoothstep(edge, edge + 0.006, r);
  float turn = fract(a / 6.283185 + 0.5);   // angle -> 0..1
  vec3 ink = mix(vec3(0.96, 0.43, 0.30), vec3(0.48, 0.83, 0.69), turn);
  vec3 color = mix(vec3(0.06, 0.10, 0.14), ink, mask);
  gl_FragColor = vec4(color, 1.0);
}

JS sidegl.uniform2f(uResolution, …, …)

length gives distance, atan gives angle: in polar coordinates petals, rays and spirals are one line each.

Try it

Set the petals to 3
Add a little twist to get a spiral
Find the line where the colour jumps: atan breaks at ±π