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WIP matrix & rotation lua APIs
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Lars Mueller
parent
a87ce1bad7
commit
513532a93c
15 changed files with 1509 additions and 5 deletions
287
games/devtest/mods/unittests/matrix4.lua
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287
games/devtest/mods/unittests/matrix4.lua
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local function describe(_, func)
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func()
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end
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local function it(section_name, func)
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print("Running test: " .. section_name)
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func()
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end
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local assert = require("luassert")
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local function assert_close(a, b)
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assert(a:equals(b, 1e-4))
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end
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local mat1 = Matrix4.new(
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1, 2, 3, 4,
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5, 6, 7, 8,
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9, 10, 11, 12,
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13, 14, 15, 16
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)
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it("identity", function()
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assert.equals(Matrix4.new(
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1, 0, 0, 0,
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0, 1, 0, 0,
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0, 0, 1, 0,
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0, 0, 0, 1
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), Matrix4.identity())
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end)
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describe("getters & setters", function()
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it("get & set", function()
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local mat = Matrix4.all(0)
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local i = 0
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for row = 1, 4 do
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for col = 1, 4 do
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i = i + 1
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assert.equals(0, mat:get(row, col))
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mat:set(row, col, i)
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assert.equals(i, mat:get(row, col))
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end
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end
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assert.equals(mat1, mat)
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end)
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it("get_row & set_row", function()
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local mat = mat1:copy()
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assert.same({5, 6, 7, 8}, {mat:get_row(2)})
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mat:set_row(2, 1, 2, 3, 4)
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assert.same({1, 2, 3, 4}, {mat:get_row(2)})
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end)
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it("get_column & set_column", function()
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local mat = mat1:copy()
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assert.same({3, 7, 11, 15}, {mat:get_column(3)})
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mat:set_column(3, 1, 2, 3, 4)
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assert.same({1, 2, 3, 4}, {mat:get_column(3)})
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end)
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end)
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it("copy", function()
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assert.equals(mat1, mat1:copy())
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end)
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it("unpack", function()
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assert.equals(mat1, Matrix4.new(mat1:unpack()))
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end)
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describe("transform", function()
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it("4d", function()
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assert.same({
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1 * 1 + 2 * 5 + 3 * 9 + 4 * 13,
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1 * 2 + 2 * 6 + 3 * 10 + 4 * 14,
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1 * 3 + 2 * 7 + 3 * 11 + 4 * 15,
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1 * 4 + 2 * 8 + 3 * 12 + 4 * 16,
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}, {mat1:transform_4d(1, 2, 3, 4)})
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end)
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it("position", function()
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assert.equals(vector.new(
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1 * 1 + 2 * 5 + 3 * 9,
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1 * 2 + 2 * 6 + 3 * 10,
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1 * 3 + 2 * 7 + 3 * 11
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):offset(13, 14, 15), mat1:transform_position(vector.new(1, 2, 3)))
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end)
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it("direction", function()
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assert.equals(vector.new(
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1 * 1 + 2 * 5 + 3 * 9,
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1 * 2 + 2 * 6 + 3 * 10,
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1 * 3 + 2 * 7 + 3 * 11
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), mat1:transform_direction(vector.new(1, 2, 3)))
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end)
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end)
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local mat2 = Matrix4.new(
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16, 15, 14, 13,
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12, 11, 10, 9,
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8, 7, 6, 5,
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4, 3, 2, 1
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)
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describe("composition", function()
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it("identity for empty argument list", function()
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assert(Matrix4.identity():equals(Matrix4.compose()))
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end)
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it("same matrix for single argument", function()
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local mat = Matrix4.new(
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1, 2, 3, 4,
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5, 6, 7, 8,
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9, 10, 11, 12,
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13, 14, 15, 16
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)
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assert(mat:equals(mat:compose()))
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end)
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it("matrix multiplication for two arguments", function()
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local composition = mat1:compose(mat2)
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assert.equals(Matrix4.new(
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386, 444, 502, 560,
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274, 316, 358, 400,
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162, 188, 214, 240,
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50, 60, 70, 80
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), composition)
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assert.same({mat1:transform_4d(mat2:transform_4d(1, 2, 3, 4))},
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{composition:transform_4d(1, 2, 3, 4)})
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end)
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it("supports multiple arguments", function()
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local fib = Matrix4.new(
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0, 1, 0, 0, -- x' = y
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1, 1, 0, 0, -- y' = x + y
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0, 0, 1, 0,
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0, 0, 0, 1
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)
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local function rep(v, n)
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if n == 0 then
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return
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end
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return v, rep(v, n - 1)
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end
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local result = Matrix4.compose(rep(fib, 10))
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assert.equals(55, result:get(2, 1))
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end)
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end)
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local function random_matrix4()
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local t = {}
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for i = 1, 16 do
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t[i] = math.random()
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end
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return Matrix4.new(unpack(t))
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end
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it("determinant", function()
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assert.equal(42, Matrix4.scale(vector.new(2, 3, 7)):determinant())
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end)
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describe("inversion", function()
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it("simple permutation", function()
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assert_close(Matrix4.new(
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0, 1, 0, 0,
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0, 0, 1, 0,
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1, 0, 0, 0,
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0, 0, 0, 1
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), Matrix4.new(
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0, 0, 1, 0,
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1, 0, 0, 0,
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0, 1, 0, 0,
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0, 0, 0, 1
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):invert())
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end)
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it("random matrices", function()
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for _ = 1, 100 do
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local mat = random_matrix4()
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if math.abs(mat:determinant()) > 1e-3 then
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assert_close(Matrix4.identity(), mat:invert():compose(mat))
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assert_close(Matrix4.identity(), mat:compose(mat:invert()))
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end
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end
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end)
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end)
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it("transpose", function()
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assert.equals(Matrix4.new(
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1, 5, 9, 13,
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2, 6, 10, 14,
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3, 7, 11, 15,
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4, 8, 12, 16
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), mat1:transpose())
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end)
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describe("affine transform constructors", function()
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it("translation", function()
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assert.equals(Matrix4.new(
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1, 0, 0, 0,
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0, 1, 0, 0,
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0, 0, 1, 0,
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1, 2, 3, 1
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), Matrix4.translation(vector.new(1, 2, 3)))
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end)
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it("scale", function()
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assert.equals(Matrix4.new(
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-1, 0, 0, 0,
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0, 2, 0, 0,
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0, 0, 3, 0,
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0, 0, 0, 1
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), Matrix4.scale(vector.new(-1, 2, 3)))
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end)
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it("rotation", function()
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assert_close(Matrix4.new(
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0, -1, 0, 0,
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1, 0, 0, 0,
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0, 0, 1, 0,
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0, 0, 0, 1
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), Matrix4.rotation(Rotation.z(math.pi / 2)))
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end)
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it("reflection", function()
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assert_close(Matrix4.identity() - 2/(1^2 + 2^2 + 3^2) * Matrix4.new(
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1, 2, 3, 0,
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2, 4, 6, 0,
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3, 6, 9, 0,
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0, 0, 0, 0
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), Matrix4.reflection(vector.new(1, 2, 3)))
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end)
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end)
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describe("affine transform methods", function()
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local t = vector.new(4, 5, 6)
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local r = Rotation.z(math.pi / 2)
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local s = vector.new(1, 2, 3)
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local trs = Matrix4.compose(
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Matrix4.translation(t),
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Matrix4.rotation(r),
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Matrix4.scale(s)
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)
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it("is affine", function()
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assert(trs:is_affine_transform())
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assert(not mat1:is_affine_transform())
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end)
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it("get translation", function()
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assert.equals(t, trs:get_translation())
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end)
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it("get rotation & scale", function()
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print(trs)
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local rotation, scale = trs:get_rs()
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print(rotation, scale)
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print(r)
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assert(r:angle_to(rotation) < 1e-4)
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assert(s:distance(scale) < 1e-4)
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end)
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it("set translation", function()
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local mat = trs:copy()
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local v = vector.new(1, 2, 3)
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mat:set_translation(v)
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assert.equals(v, mat:get_translation())
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end)
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end)
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describe("metamethods", function()
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it("addition", function()
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assert.equals(Matrix4.all(17), mat1 + mat2)
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end)
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it("subtraction", function()
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assert.equals(Matrix4.all(0), mat1 - mat1)
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end)
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it("unary minus", function()
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assert.equals(-1 * mat1, -mat1)
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end)
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it("scalar multiplication", function()
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assert.equals(2 * mat1, mat1 * 2)
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assert.equals(2 * mat1, mat1:compose(Matrix4.new(
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2, 0, 0, 0,
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0, 2, 0, 0,
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0, 0, 2, 0,
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0, 0, 0, 2
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)))
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end)
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it("equals", function()
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local mat1 = Matrix4.identity()
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local mat2 = Matrix4.identity()
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assert(mat1:equals(mat2))
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mat2:set(1, 1, 0)
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assert(not mat1:equals(mat2))
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mat2:set(1, 1, 0.999)
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assert(mat1:equals(mat2, 0.01))
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end)
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it("tostring", function()
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assert(tostring(Matrix4.scale(vector.new(12345, 0, 0))):find"12345")
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end)
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end)
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