473 lines
13 KiB
Lua
473 lines
13 KiB
Lua
--- double 4x4, 1-based, column major matrices
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-- @module mat4
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local current_folder = (...):gsub('%.[^%.]+$', '') .. "."
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local constants = require(current_folder .. "constants")
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local vec2 = require(current_folder .. "vec2")
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local vec3 = require(current_folder .. "vec3")
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local quat = require(current_folder .. "quat")
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local mat4 = {}
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-- Private constructor.
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local function new(m)
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m = m or {
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0, 0, 0, 0,
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0, 0, 0, 0,
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0, 0, 0, 0,
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0, 0, 0, 0
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}
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m._m = m
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return setmetatable(m, vec3_mt)
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end
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-- Do the check to see if JIT is enabled. If so use the optimized FFI structs.
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local status, ffi
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if type(jit) == "table" and jit.status() then
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status, ffi = pcall(require, "ffi")
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if status then
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ffi.cdef "typedef struct { double _m[16]; } cpml_mat4;"
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new = ffi.typeof("cpml_mat4")
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end
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end
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function mat4.new(v)
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local o = new()
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local m = o._m
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if type(v) == "table" and #v == 16 then
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for i=1,16 do
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m[i] = tonumber(v[i])
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end
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elseif type(v) == "table" and #v == 9 then
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m[1], m[2], m[3] = v[1], v[2], v[3]
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m[5], m[6], m[7] = v[4], v[5], v[6]
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m[9], m[10], m[11] = v[7], v[8], v[9]
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m[16] = 1
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elseif type(v) == "table" and type(v[1]) == "table" then
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local idx = 1
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for i=1, 4 do
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for j=1, 4 do
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m[idx] = v[i][j]
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idx = idx + 1
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end
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end
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else
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m[1] = 1
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m[6] = 1
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m[11] = 1
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m[16] = 1
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end
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return o
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end
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local temp = mat4.new()
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function mat4:clone()
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return new(self._m)
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end
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function mat4.from_axis_angle(angle, axis)
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if type(angle) == "table" then
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angle, axis = angle:to_axis_angle()
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end
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local l = axis:len()
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if l == 0 then
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return self
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end
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local x, y, z = axis.x / l, axis.y / l, axis.z / l
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local c = math.cos(angle)
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local s = math.sin(angle)
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local m = {
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x*x*(1-c)+c, y*x*(1-c)+z*s, x*z*(1-c)-y*s, 0,
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x*y*(1-c)-z*s, y*y*(1-c)+c, y*z*(1-c)+x*s, 0,
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x*z*(1-c)+y*s, y*z*(1-c)-x*s, z*z*(1-c)+c, 0,
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0, 0, 0, 1,
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}
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return new(m)
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end
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function mat4.from_direction(direction, up)
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local forward = direction:normalize()
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local side = forward:cross(up):normalize()
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local new_up = side:cross(forward):normalize()
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local view = mat4.new()
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local m = view._m
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m[1] = side.x
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m[5] = side.y
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m[9] = side.z
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m[2] = new_up.x
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m[6] = new_up.y
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m[10] = new_up.z
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m[3] = forward.x
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m[7] = forward.y
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m[11] = forward.z
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m[16] = 1
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return view
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end
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function mat4.from_perspective(fovy, aspect, near, far)
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assert(aspect ~= 0)
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assert(near ~= far)
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local t = math.tan(math.rad(fovy) / 2)
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local result = {
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0, 0, 0, 0,
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0, 0, 0, 0,
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0, 0, 0, 0,
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0, 0, 0, 0
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}
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result[1] = 1 / (t * aspect)
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result[6] = 1 / t
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result[11] = -(far + near) / (far - near)
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result[12] = -1
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result[15] = -(2 * far * near) / (far - near)
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result[16] = 1
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return mat4.new(result)
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end
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function mat4.from_ortho(left, right, top, bottom, near, far)
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local out = mat4.new()
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out[1] = 2 / (right - left)
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out[6] = 2 / (top - bottom)
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out[11] = -2 / (far - near)
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out[13] = -((right + left) / (right - left))
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out[14] = -((top + bottom) / (top - bottom))
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out[15] = -((far + near) / (far - near))
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out[16] = 1
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return out
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end
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-- Adapted from the Oculus SDK.
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function mat4.from_hmd_perspective(tanHalfFov, zNear, zFar, flipZ, farAtInfinity)
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-- CPML is right-handed and intended for GL, so these don't need to be arguments.
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local rightHanded = true
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local isOpenGL = true
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local function CreateNDCScaleAndOffsetFromFov(tanHalfFov)
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x_scale = 2 / (tanHalfFov.LeftTan + tanHalfFov.RightTan)
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x_offset = (tanHalfFov.LeftTan - tanHalfFov.RightTan) * x_scale * 0.5
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y_scale = 2 / (tanHalfFov.UpTan + tanHalfFov.DownTan )
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y_offset = (tanHalfFov.UpTan - tanHalfFov.DownTan ) * y_scale * 0.5
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local result = {
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Scale = vec2(x_scale, y_scale),
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Offset = vec2(x_offset, y_offset)
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}
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-- Hey - why is that Y.Offset negated?
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-- It's because a projection matrix transforms from world coords with Y=up,
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-- whereas this is from NDC which is Y=down.
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return result
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end
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if not flipZ and farAtInfinity then
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print("Error: Cannot push Far Clip to Infinity when Z-order is not flipped")
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farAtInfinity = false
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end
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-- A projection matrix is very like a scaling from NDC, so we can start with that.
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local scaleAndOffset = CreateNDCScaleAndOffsetFromFov(tanHalfFov)
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local handednessScale = rightHanded and -1.0 or 1.0
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local projection = mat4.new()
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-- Produces X result, mapping clip edges to [-w,+w]
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projection[1] = scaleAndOffset.Scale.x
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projection[2] = 0
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projection[3] = handednessScale * scaleAndOffset.Offset.x
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projection[4] = 0
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-- Produces Y result, mapping clip edges to [-w,+w]
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-- Hey - why is that YOffset negated?
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-- It's because a projection matrix transforms from world coords with Y=up,
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-- whereas this is derived from an NDC scaling, which is Y=down.
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projection[5] = 0
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projection[6] = scaleAndOffset.Scale.y
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projection[7] = handednessScale * -scaleAndOffset.Offset.y
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projection[8] = 0
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-- Produces Z-buffer result - app needs to fill this in with whatever Z range it wants.
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-- We'll just use some defaults for now.
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projection[9] = 0
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projection[10] = 0
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if farAtInfinity then
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if isOpenGL then
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-- It's not clear this makes sense for OpenGL - you don't get the same precision benefits you do in D3D.
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projection[11] = -handednessScale
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projection[12] = 2.0 * zNear
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else
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projection[11] = 0
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projection[12] = zNear
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end
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else
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if isOpenGL then
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-- Clip range is [-w,+w], so 0 is at the middle of the range.
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projection[11] = -handednessScale * (flipZ and -1.0 or 1.0) * (zNear + zFar) / (zNear - zFar)
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projection[12] = 2.0 * ((flipZ and -zFar or zFar) * zNear) / (zNear - zFar)
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else
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-- Clip range is [0,+w], so 0 is at the start of the range.
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projection[11] = -handednessScale * (flipZ and -zNear or zFar) / (zNear - zFar)
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projection[12] = ((flipZ and -zFar or zFar) * zNear) / (zNear - zFar)
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end
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end
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-- Produces W result (= Z in)
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projection[13] = 0
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projection[14] = 0
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projection[15] = handednessScale
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projection[16] = 0
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return projection:transpose()
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end
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function mat4.compose_world_matrix(t, rot, scale)
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local angle, axis = rot:to_axis_angle()
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local l = axis:len()
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if l == 0 then
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return self
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end
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local x, y, z = axis.x / l, axis.y / l, axis.z / l
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local c = math.cos(angle)
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local s = math.sin(angle)
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local m = {
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x*x*(1-c)+c, y*x*(1-c)+z*s, x*z*(1-c)-y*s, 0,
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x*y*(1-c)-z*s, y*y*(1-c)+c, y*z*(1-c)+x*s, 0,
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x*z*(1-c)+y*s, y*z*(1-c)-x*s, z*z*(1-c)+c, 0,
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t.x, t.y, t.z, 1,
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}
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return new(m)
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end
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function mat4:to_quat()
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local m = self:transpose():to_vec4s()
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print(m[1][1], m[2][2], m[3][3])
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local w = math.sqrt(1 + m[1][1] + m[2][2] + m[3][3]) / 2
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local scale = w * 4
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return quat.new(
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m[3][2] - m[2][3] / scale,
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m[1][3] - m[3][1] / scale,
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m[2][1] - m[1][2] / scale,
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w
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):normalize()
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end
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function mat4.mul(out, a, b)
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out[1] = a[1]*b[1]+a[2]*b[5]+a[3]*b[9]+a[4]*b[13]
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out[2] = a[1]*b[2]+a[2]*b[6]+a[3]*b[10]+a[4]*b[14]
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out[3] = a[1]*b[3]+a[2]*b[7]+a[3]*b[11]+a[4]*b[15]
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out[4] = a[1]*b[4]+a[2]*b[8]+a[3]*b[12]+a[4]*b[16]
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out[5] = a[5]*b[1]+a[6]*b[5]+a[7]*b[9]+a[8]*b[13]
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out[6] = a[5]*b[2]+a[6]*b[6]+a[7]*b[10]+a[8]*b[14]
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out[7] = a[5]*b[3]+a[6]*b[7]+a[7]*b[11]+a[8]*b[15]
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out[8] = a[5]*b[4]+a[6]*b[8]+a[7]*b[12]+a[8]*b[16]
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out[9] = a[9]*b[1]+a[10]*b[5]+a[11]*b[9]+a[12]*b[13]
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out[10] = a[9]*b[2]+a[10]*b[6]+a[11]*b[10]+a[12]*b[14]
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out[11] = a[9]*b[3]+a[10]*b[7]+a[11]*b[11]+a[12]*b[15]
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out[12] = a[9]*b[4]+a[10]*b[8]+a[11]*b[12]+a[12]*b[16]
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out[13] = a[13]*b[1]+a[14]*b[5]+a[15]*b[9]+a[16]*b[13]
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out[14] = a[13]*b[2]+a[14]*b[6]+a[15]*b[10]+a[16]*b[14]
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out[15] = a[13]*b[3]+a[14]*b[7]+a[15]*b[11]+a[16]*b[15]
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out[16] = a[13]*b[4]+a[14]*b[8]+a[15]*b[12]+a[16]*b[16]
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return out
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end
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function mat4.translate(out, a, t)
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local m = 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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t.x, t.y, t.z, 1
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}
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return mat4.mul(out, a, m)
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end
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function mat4.scale(out, a, s)
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local m = new {
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s.x, 0, 0, 0,
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0, s.y, 0, 0,
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0, 0, s.z, 0,
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0, 0, 0, 1
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}
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return mat4.mul(out, a, m)
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end
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-- Inverse of matrix. Tested OK
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function mat4:invert()
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local out = mat4()
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out[1] = self[6] * self[11] * self[16] - self[6] * self[12] * self[15] -
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self[10] * self[7] * self[16] + self[10] * self[8] * self[15] + self[14]
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* self[7] * self[12] - self[14] * self[8] * self[11]
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out[5] = -self[5] * self[11] * self[16] + self[5] * self[12] * self[15] +
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self[9] * self[7] * self[16] - self[9] * self[8] * self[15] - self[13] *
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self[7] * self[12] + self[13] * self[8] * self[11]
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out[9] = self[5] * self[10] * self[16] - self[5] * self[12] * self[14] -
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self[9] * self[6] * self[16] + self[9] * self[8] * self[14] + self[13] *
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self[6] * self[12] - self[13] * self[8] * self[10]
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out[13] = -self[5] * self[10] * self[15] + self[5] * self[11] * self[14] +
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self[9] * self[6] * self[15] - self[9] * self[7] * self[14] - self[13 *
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self[6] * self[11] + self[13] * self[7] * self[10]
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out[2] = -self[2] * self[11] * self[16] + self[2] * self[12] * self[15] +
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self[10] * self[3] * self[16] - self[10] * self[4] * self[15] - self[14] *
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self[3] * self[12] +self[14] * self[4] * self[11]
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out[6] = self[1] * self[11] * self[16] - self[1] * self[12] * self[15] -
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self[9] * self[3] * self[16] + self[9] * self[4] * self[15] + self[13] *
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self[3] * self[12] - self[13] * self[4] * self[11]
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out[10] = -self[1] * self[10] * self[16] + self[1] * self[12] * self[14] +
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self[9] * self[2] * self[16] - self[9] * self[4] * self[14] - self[13] *
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self[2] * self[12] + self[13] * self[4] * self[10]
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out[14] = self[1] * self[10] * self[15] - self[1] * self[11] * self[14] -
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self[9] * self[2] * self[15] + self[9] * self[3] * self[14] + self[13] *
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self[2] * self[11] - self[13] * self[3] * self[10]
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out[3] = self[2] * self[7] * self[16] - self[2] * self[8] * self[15] -
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self[6] * self[3] * self[16] + self[6] * self[4] * self[15] + self[14] *
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self[3] * self[8] - self[14] * self[4] * self[7]
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out[7] = -self[1] * self[7] * self[16] + self[1] * self[8] * self[15] +
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self[5] * self[3] * self[16] - self[5] * self[4] * self[15] - self[13] *
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self[3] * self[8] + self[13] * self[4] * self[7]
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out[11] = self[1] * self[6] * self[16] - self[1] * self[8] * self[14] -
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self[5] * self[2] * self[16] + self[5] * self[4] * self[14] + self[13] *
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self[2] * self[8] - self[13] * self[4] * self[6]
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out[15] = -self[1] * self[6] * self[15] + self[1] * self[7] * self[14] +
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self[5] * self[2] * self[15] - self[5] * self[3] * self[14] - self[13] *
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self[2] * self[7] + self[13] * self[3] * self[6]
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out[4] = -self[2] * self[7] * self[12] + self[2] * self[8] * self[11] +
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self[6] * self[3] * self[12] - self[6] * self[4] * self[11] - self[10] *
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self[3] * self[8] + self[10] * self[4] * self[7]
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out[8] = self[1] * self[7] * self[12] - self[1] * self[8] * self[11] -
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self[5] * self[3] * self[12] + self[5] * self[4] * self[11] +self[9] *
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self[3] * self[8] - self[9] * self[4] * self[7]
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out[12] = -self[1] * self[6] * self[12] + self[1] * self[8] * self[10] +
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self[5] * self[2] * self[12] - self[5] * self[4] * self[10] - self[9] *
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self[2] * self[8] + self[9] * self[4] * self[6]
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out[16] = self[1] * self[6] * self[11] - self[1] * self[7] * self[10] -
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self[5] * self[2] * self[11] + self[5] * self[3] * self[10] + self[9] *
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self[2] * self[7] - self[9] * self[3] * self[6]
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local det = self[1] * out[1] + self[2] * out[5] + self[3] * out[9] + self[4] * out[13]
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if det == 0 then return self end
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det = 1.0 / det
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for i = 1, 16 do
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out[i] = out[i] * det
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end
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return out
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end
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function mat4:look_at(eye, center, up)
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local forward = (center - eye):normalize()
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local side = forward:cross(up):normalize()
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local new_up = side:cross(forward):normalize()
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local view = mat4()
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view[1] = side.x
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view[5] = side.y
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view[9] = side.z
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view[2] = new_up.x
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view[6] = new_up.y
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view[10] = new_up.z
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view[3] = -forward.x
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view[7] = -forward.y
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view[11] = -forward.z
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view[16] = 1
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local out = mat4():translate(-eye - forward) * view
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return out * self
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end
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function mat4.transpose(out, a)
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return new {
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self[1], self[5], self[9], self[13],
|
|
self[2], self[6], self[10], self[14],
|
|
self[3], self[7], self[11], self[15],
|
|
self[4], self[8], self[12], self[16]
|
|
}
|
|
out[1] = a[1]
|
|
out[2] = a[5]
|
|
out[3] = a[9]
|
|
return mat4(m)
|
|
end
|
|
|
|
|
|
function mat4:__eq(b)
|
|
local abs = math.abs
|
|
for i=1, 16 do
|
|
if then
|
|
return false
|
|
end
|
|
end
|
|
return true
|
|
end
|
|
|
|
function mat4:__tostring()
|
|
local str = "[ "
|
|
for i, v in ipairs(self) do
|
|
str = str .. string.format("%2.5f", v)
|
|
if i < #self then
|
|
str = str .. ", "
|
|
end
|
|
end
|
|
str = str .. " ]"
|
|
return str
|
|
end
|
|
|
|
function mat4:__unm()
|
|
return self:invert()
|
|
end
|
|
|
|
-- Multiply mat4 by a mat4. Tested OK
|
|
function mat4:__mul(m)
|
|
if #m == 4 then
|
|
local tmp = matrix_mult_nxn(self:transpose():to_vec4s(), { {m[1]}, {m[2]}, {m[3]}, {m[4]} })
|
|
local v = {}
|
|
for i=1, 4 do
|
|
v[i] = tmp[i][1]
|
|
end
|
|
return v
|
|
end
|
|
|
|
|
|
end
|
|
|
|
return mat4
|