geometrymath

Linear algebra library for computer graphics and robotics applications.

Vectors

The Vec2, Vec3 and Vec4 types are used to represent float64 vectors.

let
  a = Vec2(x: 1, y: 2)
  b = Vec2(x: 3, y: 4)

echo 2.0 * a # (x: 2.0, y: 4.0)
echo a + b # (x: 4.0, y: 6.0)

echo dot(a, b) # 11.0
echo b.length() # 5.0
echo b.normalize() # (x: 0.6, y: 0.8)

echo a[AxisX] # 1.0

The Index2, Index3 and Index4 are vectors of type int.

let
  a = Index2(x: 1, y: 2)
  b = Index2(x: 3, y: 4)

echo 2 * a # (x: 2, y: 4)
echo a + b # (x: 4, y: 6)
echo a.toVec2() # (x: 1.0, y: 2.0)

Matrices

Matrices are represented using the StaticMatrix[T; H, W: static[int]] type. The Mat2, Mat3 and Mat4 type aliases represent square matrices of type float64.

let
  a = Mat2.identity()
  b = Mat2.init([float64 1, 2, 3, 4])
  c = StaticMatrix[float64, 2, 3].init([float64 1, 2, 3, 4, 5, 6])

echo a # [1.0, 0.0; 0.0, 1.0]

echo b * c # [9.0, 12.0, 15.0; 19.0, 26.0, 33.0]
echo b.det() # -2.0
echo c.transpose() # [1.0, 4.0; 2.0, 5.0; 3.0, 6.0]

echo b[0, 1] # 2.0
echo c[0..1, 0..1] # [1.0, 2.0; 4.0, 5.0]

echo Mat3.rotateZ(Deg(90))
# [6.123233995736766e-17, -1.0,                  0.0;
#  1.0,                   6.123233995736766e-17, 0.0;
#  0.0,                   0.0,                   1.0]

Bounding Boxes

let box = Box2(
  min: Vec2(x: 1, y: 2),
  max: Vec2(x: 3, y: 4)
)

echo box.center # (x: 2.0, y: 3.0)
echo box.size # (x: 2.0, y: 2.0)

echo box.xInter # (min: 1.0, max: 3.0)
echo box.yInter # (min: 2.0, max: 4.0)

A 1-dimensional bounding box is called an interval.

let inter = Inter(min: 1, max: 2)
echo inter.size # 1.0
echo inter.center # 1.5

Angles

echo Deg(90) # 90.0°
echo Rad(PI / 2) # 1.570796326794897rad

echo Rad(PI).toDeg() # 180.0°
echo sin(Deg(90)) # 1.0

echo Mat2.rotate(Deg(90))
# [6.123233995736766e-17, -1.0;
#  1.0,                   6.123233995736766e-17]

License