Core math API used by the script system. It can be accessed using the math interface and consists of a number of constants, functions, and built-in vector and matrix types.
Basic Types
Basic math types available to the script system include:
- int - 32-bit signed integer
- uint - 32-bit unsigned integer
- float - 32-bit floating point value
Vector and Matrix Types
- float2, float3, float4 - vector types of the indicated size. A float3, for example, consists of 3 floats in vector format. Components can be accessed as x, y, z, w or by index (see the examples below). GLSL style swizzling is supported, as well as array syntax. Swizzling can be used to copy out smaller vectors as well.
- float2x2, float3x3, float4x4 - matrix types of the indicated size (2x2, 3x3, or 4x4 matrix). Rows can be accessed using the array syntax and are of the associated vector type (float2x2 = 2 x float2).
Vector Operations
Vector types (float, float2, float3, float4) can be referenced using array and component syntax. Swizzling is supported.
Example Swizzles:
float2 v(1, 2);
system.print("{}", v); // (1, 2)
system.print("{}", v.yx); // (2, 1)
system.print("{}", v.xx); // (1, 1)
float a = v.y;
system.print("{}", a); // 2
float3 v3(1, 2, 3);
float2 v2 = v3.xz;
Example of Array Access:
float2 v2(2,3);
system.print("{}", v2[0]); // 2
system.print("{}", v2[1]); // 3
float4 v4(1, 2, 3, 4);
system.print("{}", v4[1]); // 2
system.print("{}", v4[3]); // 4
Example of mathematical operations, basic operations are supported:
float2 a(1,2); float2 b(2,3); float4 a4(1,2,3,4); float2 c = a + b; // c = (1,2) + (2,3) = (3,5) float2 d = a * b; // d = (1,2) * (2,3) = (2,6) float2 e = a * 2.0; // e = (1,2) * 2 = (2,4) float3 f = a4.xyz * a.y; // f = (1,2,3) * (2) = (2,4,6)
Matrix Operations
Matrices are stored as a series of vectors, which can be accessed using array syntax. Matrix types support matrix/matrix and matrix/vector multiplication, as well as matrix/float scaling. The following types are supported: float2x2, float3x3, float4x4.
float2x2 m2x2(1, 0, 0, 1); // 2x2 matrix: [1 0]
[0 1]
float3x3 m0(float3(1, 0, 0), float3(0, 1, 0), float3(0, 0, 1)); // 3x3 identity.
float3x3 m1;
float3x3 m2 = m0 * m1; // concatenate matrices m0 and m1.
float3 pos;
float3 r = m2 * pos; // multiply 'pos' by matrix m2.
float3 v = m0[1]; // v = (0, 1, 0)
float2x2 rot2x2 = math.rotationMatrix2x2(angle);
float3x3 rot3x3 = math.rotationMatrix3x3(pitch, yaw, roll);
// Transform a 2D point.
float2 point;
float2 pivot; // center point of rotation.
float2 rotatedPoint = rot2x2 * (point - pivot) + pivot;
Math Examples
float2 s(2, 3); float2 t(4, 5); float2 q(3, 4); float3 r(4, 5, 6); float3 color0(1.0, 0.5, 0.5); float3 color1(0.25, 0.25, 1.0); float dist = math.distance(s, q); // distance between (2,3) and (3,4). float blend = math.smoothstep(0, 5, dist); // produce a blend factor between [0,1] float2 value = math.mix(s, t, blend); float2 sum = r.xy + r.yz; float3 unit = math.normalize(r); float3 color = math.mix(color0, color1, blend);
Math Constants
| Constant | Description |
|---|---|
| float pi | value of π |
| float twoPi | value of 2*π |
| float e | value of the natural number e |