Added transformation operations
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src/transformations.nim
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129
src/transformations.nim
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import "./tuple"
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import "./matrix"
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import math
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proc translation*(x, y, z: float): Matrix = matrix(@[1.0, 0.0, 0.0, x, 0.0, 1.0, 0.0, y, 0.0, 0.0, 1.0, z, 0.0, 0.0, 0.0, 1.0], 4, 4)
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proc scaling*(x, y, z: float): Matrix = matrix(@[x, 0.0, 0.0, 0.0, 0.0, y, 0.0, 0.0, 0.0, 0.0, z, 0.0, 0.0, 0.0, 0.0, 1.0], 4, 4)
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proc rotationX*(radians: float): Matrix = matrix(@[1.0, 0.0, 0.0, 0.0, 0.0, cos(radians), -sin(radians), 0.0, 0.0, sin(radians), cos(radians), 0.0, 0.0, 0.0, 0.0, 1.0], 4, 4)
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proc rotationY*(radians: float): Matrix = matrix(@[cos(radians), 0.0, sin(radians), 0.0, 0.0, 1.0, 0.0, 0.0, -sin(radians), 0.0, cos(radians), 0.0, 0.0, 0.0, 0.0, 1.0], 4, 4)
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proc rotationZ*(radians: float): Matrix = matrix(@[cos(radians), -sin(radians), 0.0, 0.0, sin(radians), cos(radians), 0.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0], 4, 4)
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proc shearing*(x_y, x_z, y_x, y_z, z_x, z_y: float): Matrix = matrix(@[1.0, x_y, x_z, 0.0, y_x, 1.0, y_z, 0.0, z_x, z_y, 1.0, 0.0, 0.0, 0.0, 0.0, 1.0], 4, 4)
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when isMainModule:
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import unittest
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suite "transformations":
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test "Multiplying by a translation matrix":
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let transform = translation(5.0, -3.0, 2.0)
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let p = point(-3.0, 4.0, 5.0)
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check(transform * p == point(2.0, 1.0, 7.0))
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test "Multiplying by the inverse of a translation matrix":
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let transform = translation(5.0, -3.0, 2.0).inverse()
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let p = point(-3.0, 4.0, 5.0)
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check(transform * p == point(-8.0, 7.0, 3.0))
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test "Translation does not affect vectors":
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let transform = translation(5.0, -3.0, 2.0)
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let v = vector(-3.0, 4.0, 5.0)
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check(transform * v == v)
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test "Scaling matrix applied to a point":
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let transform = scaling(2.0, 3.0, 4.0)
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let p = point(-4.0, 6.0, 8.0)
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check(transform * p == point(-8.0, 18.0, 32.0))
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test "Scaling matrix applied to a vector":
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let transform = scaling(2.0, 3.0, 4.0)
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let v = vector(-4.0, 6.0, 8.0)
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check(transform * v == vector(-8.0, 18.0, 32.0))
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test "Multiplying by the inverse of a scaling matrix":
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let transform = scaling(2.0, 3.0, 4.0).inverse()
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let v = vector(-4.0, 6.0, 8.0)
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check(transform * v == vector(-2.0, 2.0, 2.0))
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test "Reflection is scaling by a negative value":
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let transform = scaling(-1.0, 1.0, 1.0)
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let p = point(2.0, 3.0, 4.0)
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check(transform * p == point(-2.0, 3.0, 4.0))
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test "Rotation around the X axis":
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let p = point(0.0, 1.0, 0.0)
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let halfQuarter = rotationX(PI / 4)
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let fullQuarter = rotationX(PI / 2)
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check(halfQuarter * p == point(0.0, sqrt(2.0)/2.0, sqrt(2.0)/2.0))
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check(fullQuarter * p == point(0.0, 0.0, 1.0))
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test "Inverse of a rotation rotates in the opposite direction":
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let p = point(0.0, 1.0, 0.0)
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let halfQuarter = rotationX(PI / 4).inverse()
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check(halfQuarter * p == point(0.0, sqrt(2.0)/2.0, -sqrt(2.0)/2.0))
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test "Rotation around the Y axis":
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let p = point(0.0, 0.0, 1.0)
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let halfQuarter = rotationY(PI / 4)
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let fullQuarter = rotationY(PI / 2)
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check(halfQuarter * p == point(sqrt(2.0)/2.0, 0.0, sqrt(2.0)/2.0))
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check(fullQuarter * p == point(1.0, 0.0, 0.0))
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test "Rotation around the Z axis":
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let p = point(0.0, 1.0, 0.0)
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let halfQuarter = rotationZ(PI / 4)
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let fullQuarter = rotationZ(PI / 2)
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check(halfQuarter * p == point(-sqrt(2.0)/2.0, sqrt(2.0)/2.0, 0.0))
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check(fullQuarter * p == point(-1.0, 0.0, 0.0))
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test "Shearing transformation moves X in proportion to Y":
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let t = shearing(1.0, 0.0, 0.0, 0.0, 0.0, 0.0)
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let p = point(2.0, 3.0, 4.0)
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check(t * p == point(5.0, 3.0, 4.0))
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test "Shearing transformation moves X in proportion to Z":
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let t = shearing(0.0, 1.0, 0.0, 0.0, 0.0, 0.0)
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let p = point(2.0, 3.0, 4.0)
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check(t * p == point(6.0, 3.0, 4.0))
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test "Shearing transformation moves Y in proportion to X":
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let t = shearing(0.0, 0.0, 1.0, 0.0, 0.0, 0.0)
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let p = point(2.0, 3.0, 4.0)
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check(t * p == point(2.0, 5.0, 4.0))
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test "Shearing transformation moves Y in proportion to Z":
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let t = shearing(0.0, 0.0, 0.0, 1.0, 0.0, 0.0)
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let p = point(2.0, 3.0, 4.0)
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check(t * p == point(2.0, 7.0, 4.0))
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test "Shearing transformation moves Z in proportion to X":
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let t = shearing(0.0, 0.0, 0.0, 0.0, 1.0, 0.0)
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let p = point(2.0, 3.0, 4.0)
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check(t * p == point(2.0, 3.0, 6.0))
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test "Shearing transformation moves Z in proportion to Y":
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let t = shearing(0.0, 0.0, 0.0, 0.0, 0.0, 1.0)
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let p = point(2.0, 3.0, 4.0)
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check(t * p == point(2.0, 3.0, 7.0))
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test "Individual transformations applied in sequence":
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let p = point(1.0, 0.0, 1.0)
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let r = rotationX(PI / 2)
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let s = scaling(5.0, 5.0, 5.0)
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let t = translation(10.0, 5.0, 7.0)
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let p2 = r * p
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check(p2 == point(1.0, -1.0, 0.0))
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let p3 = s * p2
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check(p3 == point(5.0, -5.0, 0.0))
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let p4 = t * p3
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check(p4 == point(15.0, 0.0, 7.0))
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test "Chained transformations are applied in reverse order":
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let p = point(1.0, 0.0, 1.0)
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let r = rotationX(PI / 2)
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let s = scaling(5.0, 5.0, 5.0)
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let t = translation(10.0, 5.0, 7.0)
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let combo = t * s * r
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check(combo * p == point(15.0, 0.0, 7.0))
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