500 lines
13 KiB
Lua
500 lines
13 KiB
Lua
local ffi = require 'ffi'
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local sin = math.sin
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local cos = math.cos
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local sqrt = math.sqrt
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local abs = math.abs
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local mat4
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local vec3
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local scalar
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scalar = {
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near_equal = function(s1, s2, epsilon)
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local d = abs(s1 - s2)
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return d <= epsilon
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end,
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}
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setmetatable(scalar, scalar)
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mat4 = {
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__call = function(_t)
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-- newByteData is zero-initialized
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local data = love.data.newByteData(16 * 4)
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local m = ffi.cast('float*', data:getFFIPointer())
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value = {
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data = data,
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m = m,
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}
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setmetatable(value, mat4)
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return value
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end,
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set = function(m00, m01, m02, m03,
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m10, m11, m12, m13,
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m20, m21, m22, m23,
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m30, m31, m32, m33)
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local M = mat4()
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M.m[0 * 4 + 0] = m00
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M.m[0 * 4 + 1] = m01
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M.m[0 * 4 + 2] = m02
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M.m[0 * 4 + 3] = m03
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M.m[1 * 4 + 0] = m10
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M.m[1 * 4 + 1] = m11
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M.m[1 * 4 + 2] = m12
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M.m[1 * 4 + 3] = m13
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M.m[2 * 4 + 0] = m20
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M.m[2 * 4 + 1] = m21
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M.m[2 * 4 + 2] = m22
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M.m[2 * 4 + 3] = m23
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M.m[3 * 4 + 0] = m30
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M.m[3 * 4 + 1] = m31
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M.m[3 * 4 + 2] = m32
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M.m[3 * 4 + 3] = m33
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return M
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end,
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identity = function()
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local M = mat4()
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M.m[0 * 4 + 0] = 1.0
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--M.m[0 * 4 + 1] = 0.0
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--M.m[0 * 4 + 2] = 0.0
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--M.m[0 * 4 + 3] = 0.0
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--M.m[1 * 4 + 0] = 0.0
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M.m[1 * 4 + 1] = 1.0
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--M.m[1 * 4 + 2] = 0.0
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--M.m[1 * 4 + 3] = 0.0
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--M.m[2 * 4 + 0] = 0.0
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--M.m[2 * 4 + 1] = 0.0
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M.m[2 * 4 + 2] = 1.0
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--M.m[2 * 4 + 3] = 0.0
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--M.m[3 * 4 + 0] = 0.0
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--M.m[3 * 4 + 1] = 0.0
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--M.m[3 * 4 + 2] = 0.0
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M.m[3 * 4 + 3] = 1.0
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return M
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end,
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translation = function(x, y, z)
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local M = mat4()
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M.m[0 * 4 + 0] = 1.0
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--M.m[0 * 4 + 1] = 0.0
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--M.m[0 * 4 + 2] = 0.0
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--M.m[0 * 4 + 3] = 0.0
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--M.m[1 * 4 + 0] = 0.0
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M.m[1 * 4 + 1] = 1.0
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--M.m[1 * 4 + 2] = 0.0
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--M.m[1 * 4 + 3] = 0.0
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--M.m[2 * 4 + 0] = 0.0
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--M.m[2 * 4 + 1] = 0.0
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M.m[2 * 4 + 2] = 1.0
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--M.m[2 * 4 + 3] = 0.0
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M.m[3 * 4 + 0] = x
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M.m[3 * 4 + 1] = y
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M.m[3 * 4 + 2] = z
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M.m[3 * 4 + 3] = 1.0
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return M
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end,
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rotation_x = function(angle)
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local sin_angle = sin(angle)
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local cos_angle = cos(angle)
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local M = mat4()
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M.m[0 * 4 + 0] = 1.0
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--M.m[0 * 4 + 1] = 0.0
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--M.m[0 * 4 + 2] = 0.0
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--M.m[0 * 4 + 3] = 0.0
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--M.m[1 * 4 + 0] = 0.0
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M.m[1 * 4 + 1] = cos_angle
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M.m[1 * 4 + 2] = sin_angle
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--M.m[1 * 4 + 3] = 0.0
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--M.m[2 * 4 + 0] = 0.0
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M.m[2 * 4 + 1] = -sin_angle
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M.m[2 * 4 + 2] = cos_angle
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--M.m[2 * 4 + 3] = 0.0
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--M.m[3 * 4 + 0] = 0.0
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--M.m[3 * 4 + 1] = 0.0
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--M.m[3 * 4 + 2] = 0.0
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M.m[3 * 4 + 3] = 1.0
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return M
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end,
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rotation_y = function(angle)
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local sin_angle = sin(angle)
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local cos_angle = cos(angle)
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local M = mat4()
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M.m[0 * 4 + 0] = cos_angle
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--M.m[0 * 4 + 1] = 0.0
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M.m[0 * 4 + 2] = -sin_angle
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--M.m[0 * 4 + 3] = 0.0
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--M.m[1 * 4 + 0] = 0.0
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M.m[1 * 4 + 1] = 1.0
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--M.m[1 * 4 + 2] = 0.0
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--M.m[1 * 4 + 3] = 0.0
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M.m[2 * 4 + 0] = sin_angle
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--M.m[2 * 4 + 1] = 0.0
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M.m[2 * 4 + 2] = cos_angle
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--M.m[2 * 4 + 3] = 0.0
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--M.m[3 * 4 + 0] = 0.0
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--M.m[3 * 4 + 1] = 0.0
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--M.m[3 * 4 + 2] = 0.0
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M.m[3 * 4 + 3] = 1.0
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return M
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end,
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rotation_z = function(angle)
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local sin_angle = sin(angle)
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local cos_angle = cos(angle)
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local M = mat4()
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M.m[0 * 4 + 0] = cos_angle
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M.m[0 * 4 + 1] = sin_angle
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--M.m[0 * 4 + 2] = 0.0
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--M.m[0 * 4 + 3] = 0.0
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M.m[1 * 4 + 0] = -sin_angle
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M.m[1 * 4 + 1] = cos_angle
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--M.m[1 * 4 + 2] = 0.0
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--M.m[1 * 4 + 3] = 0.0
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--M.m[2 * 4 + 0] = 0.0
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--M.m[2 * 4 + 1] = 0.0
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M.m[2 * 4 + 2] = 1.0
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--M.m[2 * 4 + 3] = 0.0
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--M.m[3 * 4 + 0] = 0.0
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--M.m[3 * 4 + 1] = 0.0
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--M.m[3 * 4 + 2] = 0.0
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M.m[3 * 4 + 3] = 1.0
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return M
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end,
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transpose = function(M)
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local MT = mat4()
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--MT.m[0 * 4 + 0] = M.m[0 * 4 + 0]
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MT.m[0 * 4 + 1] = M.m[1 * 4 + 0]
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MT.m[0 * 4 + 2] = M.m[2 * 4 + 0]
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MT.m[0 * 4 + 3] = M.m[3 * 4 + 0]
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MT.m[1 * 4 + 0] = M.m[0 * 4 + 1]
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--MT.m[1 * 4 + 1] = M.m[1 * 4 + 1]
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MT.m[1 * 4 + 2] = M.m[2 * 4 + 1]
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MT.m[1 * 4 + 3] = M.m[3 * 4 + 1]
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MT.m[2 * 4 + 0] = M.m[0 * 4 + 2]
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MT.m[2 * 4 + 1] = M.m[1 * 4 + 2]
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--MT.m[2 * 4 + 2] = M.m[2 * 4 + 2]
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MT.m[2 * 4 + 3] = M.m[3 * 4 + 2]
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MT.m[3 * 4 + 0] = M.m[0 * 4 + 3]
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MT.m[3 * 4 + 1] = M.m[1 * 4 + 3]
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MT.m[3 * 4 + 2] = M.m[2 * 4 + 3]
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--MT.m[3 * 4 + 3] = M.m[3 * 4 + 3]
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return MT
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end,
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look_to_lh = function(eye_position, eye_direction, up_direction)
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assert(not vec3.equal(eye_direction, vec3._zero))
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assert(not vec3.isinfinite(eye_direction))
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assert(not vec3.equal(up_direction, vec3._zero))
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assert(not vec3.isinfinite(up_direction))
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local r2 = vec3.normalize(eye_direction)
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local r0 = vec3.cross(up_direction, r2)
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r0 = vec3.normalize(r0)
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local r1 = vec3.cross(r2, r0)
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local neg_eye_position = vec3.negate(eye_position)
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local d0 = vec3.dot(r0, neg_eye_position)
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local d1 = vec3.dot(r1, neg_eye_position)
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local d2 = vec3.dot(r2, neg_eye_position)
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local M = mat4()
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M.m[0 * 4 + 0] = r0.f[0]
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M.m[1 * 4 + 0] = r0.f[1]
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M.m[2 * 4 + 0] = r0.f[2]
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M.m[3 * 4 + 0] = d0
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M.m[0 * 4 + 1] = r1.f[0]
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M.m[1 * 4 + 1] = r1.f[1]
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M.m[2 * 4 + 1] = r1.f[2]
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M.m[3 * 4 + 1] = d1
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M.m[0 * 4 + 2] = r2.f[0]
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M.m[1 * 4 + 2] = r2.f[1]
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M.m[2 * 4 + 2] = r2.f[2]
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M.m[3 * 4 + 2] = d2
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--M.m[0 * 4 + 3] = 0
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--M.m[1 * 4 + 3] = 0
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--M.m[2 * 4 + 3] = 0
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M.m[3 * 4 + 3] = 1
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return M
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end,
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look_at_lh = function(eye_position, focus_position, up_direction)
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local eye_direction = vec3.subtract(focus_position, eye_position)
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return mat4.look_to_lh(eye_position, eye_direction, up_direction)
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end,
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look_at_rh = function(eye_position, focus_position, up_direction)
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local neg_eye_direction = vec3.subtract(eye_position, focus_position)
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return mat4.look_to_lh(eye_position, neg_eye_direction, up_direction)
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end,
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perspective_rh = function(view_width, view_height, near_z, far_z)
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assert(near_z > 0.0 and far_z > 0.0)
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assert(not scalar.near_equal(view_width, 0.0, 0.00001))
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assert(not scalar.near_equal(view_height, 0.0, 0.00001))
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assert(not scalar.near_equal(far_z, near_z, 0.00001))
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local two_near_z = near_z + near_z;
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local f_range = far_z / (near_z - far_z);
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local M = mat4()
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M.m[0 * 4 + 0] = two_near_z / view_width
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--M.m[0 * 4 + 1] = 0.0
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--M.m[0 * 4 + 2] = 0.0
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--M.m[0 * 4 + 3] = 0.0
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--M.m[1 * 4 + 0] = 0.0
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M.m[1 * 4 + 1] = two_near_z / view_height
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--M.m[1 * 4 + 2] = 0.0
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--M.m[1 * 4 + 3] = 0.0
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--M.m[2 * 4 + 0] = 0.0
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--M.m[2 * 4 + 1] = 0.0
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M.m[2 * 4 + 2] = f_range
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M.m[2 * 4 + 3] = -1.0
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--M.m[3 * 4 + 0] = 0.0
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--M.m[3 * 4 + 1] = 0.0
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M.m[3 * 4 + 2] = f_range * near_z
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--M.m[3 * 4 + 3] = 0.0
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return M
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end,
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near_equal = function(M1, M2, epsilon)
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local d00 = abs(M1.m[0 * 4 + 0] - M2.m[0 * 4 + 0])
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local d01 = abs(M1.m[0 * 4 + 1] - M2.m[0 * 4 + 1])
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local d02 = abs(M1.m[0 * 4 + 2] - M2.m[0 * 4 + 2])
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local d03 = abs(M1.m[0 * 4 + 3] - M2.m[0 * 4 + 3])
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local d10 = abs(M1.m[1 * 4 + 0] - M2.m[1 * 4 + 0])
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local d11 = abs(M1.m[1 * 4 + 1] - M2.m[1 * 4 + 1])
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local d12 = abs(M1.m[1 * 4 + 2] - M2.m[1 * 4 + 2])
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local d13 = abs(M1.m[1 * 4 + 3] - M2.m[1 * 4 + 3])
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local d20 = abs(M1.m[2 * 4 + 0] - M2.m[2 * 4 + 0])
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local d21 = abs(M1.m[2 * 4 + 1] - M2.m[2 * 4 + 1])
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local d22 = abs(M1.m[2 * 4 + 2] - M2.m[2 * 4 + 2])
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local d23 = abs(M1.m[2 * 4 + 3] - M2.m[2 * 4 + 3])
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local d30 = abs(M1.m[3 * 4 + 0] - M2.m[3 * 4 + 0])
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local d31 = abs(M1.m[3 * 4 + 1] - M2.m[3 * 4 + 1])
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local d32 = abs(M1.m[3 * 4 + 2] - M2.m[3 * 4 + 2])
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local d33 = abs(M1.m[3 * 4 + 3] - M2.m[3 * 4 + 3])
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return (
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(d00 <= epsilon) and (d01 <= epsilon) and (d02 <= epsilon) and (d03 <= epsilon) and
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(d10 <= epsilon) and (d11 <= epsilon) and (d12 <= epsilon) and (d13 <= epsilon) and
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(d20 <= epsilon) and (d21 <= epsilon) and (d22 <= epsilon) and (d23 <= epsilon) and
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(d30 <= epsilon) and (d31 <= epsilon) and (d32 <= epsilon) and (d33 <= epsilon)
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)
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end,
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print = function(M)
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for i = 0, 15 do
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io.write(tostring(M.m[i]))
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io.write(" ")
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if i % 4 == 3 then
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io.write("\n")
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end
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end
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end
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}
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setmetatable(mat4, mat4)
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vec3 = {
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__call = function(_t, x, y, z)
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-- newByteData is zero-initialized
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local data = love.data.newByteData(3 * 4)
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local f = ffi.cast('float*', data:getFFIPointer())
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value = {
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data = data,
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f = f,
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}
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f[0] = x or 0
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f[1] = y or 0
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f[2] = z or 0
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setmetatable(value, vec3)
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return value
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end,
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dot = function(v1, v2)
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local value = (
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v1.f[0] * v2.f[0] +
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v1.f[1] * v2.f[1] +
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v1.f[2] * v2.f[2]
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)
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return value
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end,
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length_sq = function(v)
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return vec3.dot(v, v)
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end,
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reciprocal_length = function(v)
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local result
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result = vec3.length_sq(v)
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result = 1.0 / sqrt(result)
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return result
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end,
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length = function(v)
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local result
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result = vec3.length_sq(v)
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result = sqrt(result)
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return result
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end,
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add = function(v1, v2)
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local result = vec3(
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v1.f[0] + v2.f[0],
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v1.f[1] + v2.f[1],
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v1.f[2] + v2.f[2]
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)
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return result
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end,
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subtract = function(v1, v2)
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local result = vec3(
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v1.f[0] - v2.f[0],
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v1.f[1] - v2.f[1],
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v1.f[2] - v2.f[2]
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)
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return result
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end,
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multiply = function(v1, v2)
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local result = vec3(
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v1.f[0] * v2.f[0],
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v1.f[1] * v2.f[1],
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v1.f[2] * v2.f[2]
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)
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return result
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end,
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normalize = function(v)
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local length = vec3.reciprocal_length(v)
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local result = vec3(
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v.f[0] * length,
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v.f[1] * length,
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v.f[2] * length
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)
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return result
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end,
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cross = function(v1, v2)
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local result = vec3(
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(v1.f[1] * v2.f[2]) - (v1.f[2] * v2.f[1]),
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(v1.f[2] * v2.f[0]) - (v1.f[0] * v2.f[2]),
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(v1.f[0] * v2.f[1]) - (v1.f[1] * v2.f[0])
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)
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return result
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end,
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negate = function(v)
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local result = vec3(
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-v.f[0],
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-v.f[1],
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-v.f[2]
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)
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return result
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end,
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equal = function(v1, v2)
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return (
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(v1.f[0] == v2.f[0]) and
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(v1.f[1] == v2.f[1]) and
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(v1.f[2] == v2.f[2])
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)
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end,
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near_equal = function(v1, v2, epsilon)
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local dx = abs(v1.f[0] - v2.f[0])
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local dy = abs(v1.f[1] - v2.f[1])
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local dz = abs(v1.f[2] - v2.f[2])
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return (dx <= epsilon) and (dy <= epsilon) and (dz <= epsilon)
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end,
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isinfinite = function(v)
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return (
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(v.f[0] == -math.huge or v.f[0] == math.huge) or
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(v.f[1] == -math.huge or v.f[1] == math.huge) or
|
|
(v.f[2] == -math.huge or v.f[2] == math.huge)
|
|
)
|
|
end,
|
|
|
|
print = function(v)
|
|
print(tostring(v.f[0]) .. " " .. tostring(v.f[1]) .. " " .. tostring(v.f[2]))
|
|
end,
|
|
}
|
|
|
|
setmetatable(vec3, vec3)
|
|
vec3._zero = vec3(0, 0, 0)
|
|
|
|
----------------------------------------------------------------------
|
|
-- tests
|
|
----------------------------------------------------------------------
|
|
|
|
assert(vec3.dot(vec3(1, 3, -5), vec3(4, -2, -1)) == 3)
|
|
assert(vec3.dot(vec3(1, 3, -5), vec3(1, 3, -5)) == 35)
|
|
assert(vec3.length_sq(vec3(1, 3, -5)) == 35)
|
|
assert(vec3.equal(vec3.multiply(vec3(1, 3, -5), vec3(2, 3, 4)), vec3(2, 9, -20)))
|
|
assert(vec3.near_equal(vec3.normalize(vec3(1, 3, -5)), vec3(0.16903, 0.50709, -0.84515), 0.0001))
|
|
assert(vec3.equal(vec3.cross(vec3(1, 2, 3), vec3(4, 5, 6)), vec3(-3, 6, -3)))
|
|
|
|
assert(mat4.near_equal(mat4.look_to_lh(vec3(1, 2, 3),
|
|
vec3(5, 6, 7),
|
|
vec3(9, 10, 11)),
|
|
mat4.set( 0.408249, 0.778499, 0.476731, 0.000000,
|
|
-0.816496, 0.077850, 0.572078, 0.000000,
|
|
0.408248, -0.622799, 0.667424, 0.000000,
|
|
-0.000001, 0.934199, -3.623158, 1.000000),
|
|
0.00001))
|
|
|
|
assert(mat4.near_equal(mat4.perspective_rh(2, 3, 4, 5),
|
|
mat4.set(4.000000, 0.000000, 0.000000, 0.000000,
|
|
0.000000, 2.666667, 0.000000, 0.000000,
|
|
0.000000, 0.000000, -5.000000, -1.000000,
|
|
0.000000, 0.000000, -20.000000, 0.000000),
|
|
0.00001))
|
|
|
|
return {
|
|
scalar = scalar,
|
|
mat4 = mat4,
|
|
vec3 = vec3,
|
|
}
|