Vectors and Matrices#

Adama has built-in linear algebra through the Vector and Matrix global objects. If you're building a game, doing physics simulations, or working with spatial data, this is where you look.

Vector Types#

Three vector types:

Vector Operations#

Arithmetic#

vec2 a = @vec2(1.0, 2.0);
vec2 b = @vec2(3.0, 4.0);

vec2 sum = Vector.add(a, b);        // (4.0, 6.0)
vec2 diff = Vector.sub(a, b);       // (-2.0, -2.0)
vec2 scaled = Vector.scale(2.0, a); // (2.0, 4.0)
vec2 product = Vector.cmult(a, b);  // (3.0, 8.0)

All of these work on vec2, vec3, and vec4.

Products#

vec3 a = @vec3(1.0, 0.0, 0.0);
vec3 b = @vec3(0.0, 1.0, 0.0);

double d = Vector.dot(a, b);      // 0.0
vec3 c = Vector.cross(a, b);      // (0.0, 0.0, 1.0)

Length and Normalization#

vec2 v = @vec2(3.0, 4.0);

double len = Vector.length(v);              // 5.0
maybe<vec2> unit = Vector.normalize(v);     // (0.6, 0.8)

normalize returns maybe because you can't normalize the zero vector -- there's no direction to preserve.

Utility#

Matrix Types#

Matrix Operations#

Transformation#

matrix3 rot = Matrix.to_rotation_z(1.5708);  // ~90 degrees
vec3 v = @vec3(1.0, 0.0, 0.0);
vec3 rotated = Matrix.transform(rot, v);      // ~(0.0, 1.0, 0.0)

Multiplication#

matrix3 r1 = Matrix.to_rotation_z(0.5);
matrix3 r2 = Matrix.to_rotation_z(0.5);
matrix3 combined = Matrix.multiply(r1, r2);  // rotation by 1.0 radian

Rotation Matrices#

All rotation functions also accept maybe<double> for the radians parameter.

matrix2 rot2d = Matrix.to_rotation(Math.PI() / 4.0);  // 45 degrees
matrix3 rotX = Matrix.to_rotation_x(1.0);              // 1 radian around X
matrix3 rotY = Matrix.to_rotation_y(0.5);              // 0.5 radians around Y

Inverse#

Returns maybe because singular matrices don't have inverses. That's just how math works.

matrix2 m = Matrix.to_rotation(1.0);
maybe<matrix2> inv = Matrix.inverse(m);  // inverse rotation

Conversion#

Method Summary#

Vector#

Matrix#