328 lines
12 KiB
CoffeeScript
328 lines
12 KiB
CoffeeScript
# 00 00 0000000 000000000 00000000 000 000 000
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# 000 000 000 000 000 000 000 000 000 000
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# 000000000 000000000 000 0000000 000 00000
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# 000 0 000 000 000 000 000 000 000 000 000
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# 000 000 000 000 000 000 000 000 000 000
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log = require '../tools/log'
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Quaternion = require './quaternion'
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Vector = require './vector'
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class Matrix
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constructor: (o) ->
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@matrix = []
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switch
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when not o? then @reset()
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when o instanceof Quaternion then @initQuat o
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when o instanceof Matrix then @copy o
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when o instanceof Array
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if o.length == 16
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for i in [0...16]
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@matrix[i] = o[i]
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when o?.x? and o?.y? and o?.z?
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@initXYZ o.x, o.y, o.z
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else @reset()
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initXYZ: (x,y,z) ->
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@matrix[0] = x.x
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@matrix[1] = x.y
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@matrix[2] = x.z
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@matrix[3] = x.w
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@matrix[4] = y.x
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@matrix[5] = y.y
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@matrix[6] = y.z
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@matrix[7] = y.w
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@matrix[8] = z.x
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@matrix[9] = z.y
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@matrix[11] = z.w
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@matrix[10] = z.z
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@matrix[12] = 0.0
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@matrix[13] = 0.0
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@matrix[14] = 0.0
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@matrix[15] = 1.0
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@
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initQuat: (o) ->
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# calculate coefficients
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x2 = o.x + o.x
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y2 = o.y + o.y
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z2 = o.z + o.z
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xx = o.x * x2
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xy = o.x * y2
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xz = o.x * z2
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yy = o.y * y2
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yz = o.y * z2
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zz = o.z * z2
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wx = o.w * x2
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wy = o.w * y2
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wz = o.w * z2
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@matrix[0] = 1.0 - (yy + zz)
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@matrix[1] = xy + wz
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@matrix[2] = xz - wy
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@matrix[3] = 0.0
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@matrix[4] = xy - wz
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@matrix[5] = 1.0 - (xx + zz)
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@matrix[6] = yz + wx
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@matrix[7] = 0.0
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@matrix[8] = xz + wy
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@matrix[9] = yz - wx
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@matrix[10] = 1.0 - (xx + yy)
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@matrix[11] = 0.0
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@matrix[12] = 0.0
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@matrix[13] = 0.0
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@matrix[14] = 0.0
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@matrix[15] = 1.0
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@
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copy: (m) ->
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for i in [0...16]
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@matrix[i] = m.matrix[i]
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@
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mul: (m) ->
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if m instanceof Matrix
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mm = new Matrix
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mm.matrix[0] = @matrix[0]*m.matrix[0] + @matrix[4]*m.matrix[1] + @matrix[8] *m.matrix[2] + @matrix[12]*m.matrix[3]
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mm.matrix[1] = @matrix[1]*m.matrix[0] + @matrix[5]*m.matrix[1] + @matrix[9] *m.matrix[2] + @matrix[13]*m.matrix[3]
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mm.matrix[2] = @matrix[2]*m.matrix[0] + @matrix[6]*m.matrix[1] + @matrix[10]*m.matrix[2] + @matrix[14]*m.matrix[3]
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mm.matrix[3] = @matrix[3]*m.matrix[0] + @matrix[7]*m.matrix[1] + @matrix[11]*m.matrix[2] + @matrix[15]*m.matrix[3]
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mm.matrix[4] = @matrix[0]*m.matrix[4] + @matrix[4]*m.matrix[5] + @matrix[8] *m.matrix[6] + @matrix[12]*m.matrix[7]
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mm.matrix[5] = @matrix[1]*m.matrix[4] + @matrix[5]*m.matrix[5] + @matrix[9] *m.matrix[6] + @matrix[13]*m.matrix[7]
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mm.matrix[6] = @matrix[2]*m.matrix[4] + @matrix[6]*m.matrix[5] + @matrix[10]*m.matrix[6] + @matrix[14]*m.matrix[7]
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mm.matrix[7] = @matrix[3]*m.matrix[4] + @matrix[7]*m.matrix[5] + @matrix[11]*m.matrix[6] + @matrix[15]*m.matrix[7]
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mm.matrix[8] = @matrix[0]*m.matrix[8] + @matrix[4]*m.matrix[9] + @matrix[8] *m.matrix[10] + @matrix[12]*m.matrix[11]
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mm.matrix[9] = @matrix[1]*m.matrix[8] + @matrix[5]*m.matrix[9] + @matrix[9] *m.matrix[10] + @matrix[13]*m.matrix[11]
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mm.matrix[11]= @matrix[3]*m.matrix[8] + @matrix[7]*m.matrix[9] + @matrix[11]*m.matrix[10] + @matrix[15]*m.matrix[11]
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mm.matrix[10]= @matrix[2]*m.matrix[8] + @matrix[6]*m.matrix[9] + @matrix[10]*m.matrix[10] + @matrix[14]*m.matrix[11]
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mm.matrix[12]= @matrix[0]*m.matrix[12] + @matrix[4]*m.matrix[13] + @matrix[8] *m.matrix[14] + @matrix[12]*m.matrix[15]
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mm.matrix[13]= @matrix[1]*m.matrix[12] + @matrix[5]*m.matrix[13] + @matrix[9] *m.matrix[14] + @matrix[13]*m.matrix[15]
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mm.matrix[14]= @matrix[2]*m.matrix[12] + @matrix[6]*m.matrix[13] + @matrix[10]*m.matrix[14] + @matrix[14]*m.matrix[15]
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mm.matrix[15]= @matrix[3]*m.matrix[12] + @matrix[7]*m.matrix[13] + @matrix[11]*m.matrix[14] + @matrix[15]*m.matrix[15]
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mm
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else
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new Vector @matrix[0] * v.x + @matrix[4]*v.y + @matrix[8] *v.z + @matrix[12]*v.w,
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@matrix[1] * v.x + @matrix[5]*v.y + @matrix[9] *v.z + @matrix[13]*v.w,
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@matrix[2] * v.x + @matrix[6]*v.y + @matrix[10]*v.z + @matrix[14]*v.w,
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@matrix[3] * v.x + @matrix[7]*v.y + @matrix[11]*v.z + @matrix[15]*v.w
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reset: ->
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@matrix[0] = @matrix[5] = @matrix[10] = @matrix[15] = 1.0
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@matrix[1] = @matrix[4] = @matrix[8] = @matrix[12] = 0.0
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@matrix[2] = @matrix[6] = @matrix[9] = @matrix[13] = 0.0
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@matrix[3] = @matrix[7] = @matrix[11] = @matrix[14] = 0.0
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transform: (m) -> @copy @.mul m
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translate: (x,y,z) ->
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v = new Vector x,y,z
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@matrix[12] += @matrix[0]*v.x+@matrix[4]*v.y+@matrix[8] *v.z
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@matrix[13] += @matrix[1]*v.x+@matrix[5]*v.y+@matrix[9] *v.z
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@matrix[14] += @matrix[2]*v.x+@matrix[6]*v.y+@matrix[10]*v.z
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@matrix[15] += @matrix[3]*v.x+@matrix[7]*v.y+@matrix[11]*v.z
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@rotation: (x,y,z) -> new Matrix().rotate x,y,z
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rotate: (x,y,z) ->
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rx = Vector.DEG2RAD x
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ry = Vector.DEG2RAD y
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rz = Vector.DEG2RAD z
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cx = Math.cos rx
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sx = Math.sin rx
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cy = Math.cos ry
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sy = Math.sin ry
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cz = Math.cos rz
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sz = Math.sin rz
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b0 = cy*cz
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b1 = sx*sy*cz+cx*sz
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b2 = -cx*sy*cz+sx*sz
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b4 = -cy*sz
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b5 = -sx*sy*sz+cx*cz
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b6 = cx*sy*sz+sx*cz
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b8 = sy
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b9 = -sx*cy
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b10 = cx*cy
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a0 = @matrix[0]
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a1 = @matrix[1]
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a2 = @matrix[2]
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a3 = @matrix[3]
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a4 = @matrix[4]
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a5 = @matrix[5]
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a6 = @matrix[6]
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a7 = @matrix[7]
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a8 = @matrix[8]
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a9 = @matrix[9]
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a10 = @matrix[10]
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a11 = @matrix[11]
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@matrix[0] = a0*b0+a4*b1+a8*b2
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@matrix[1] = a1*b0+a5*b1+a9*b2
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@matrix[2] = a2*b0+a6*b1+a10*b2
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@matrix[3] = a3*b0+a7*b1+a11*b2
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@matrix[4] = a0*b4+a4*b5+a8*b6
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@matrix[5] = a1*b4+a5*b5+a9*b6
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@matrix[6] = a2*b4+a6*b5+a10*b6
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@matrix[7] = a3*b4+a7*b5+a11*b6
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@matrix[8] = a0*b8+a4*b9+a8*b10
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@matrix[9] = a1*b8+a5*b9+a9*b10
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@matrix[10] = a2*b8+a6*b9+a10*b10
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@matrix[11] = a3*b8+a7*b9+a11*b10
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scale: (x,y,z) ->
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@matrix[0] *= x
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@matrix[1] *= x
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@matrix[2] *= x
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@matrix[3] *= x
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@matrix[4] *= y
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@matrix[5] *= y
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@matrix[6] *= y
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@matrix[7] *= y
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@matrix[8] *= z
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@matrix[9] *= z
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@matrix[10] *= z
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@matrix[11] *= z
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@COFACTOR_4X4_IJ: (fac,m,i,j) ->
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ii = [0,0,0,0]
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jj = [0,0,0,0]
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for k in [0...i] # compute which row, columnt to skip
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ii[k] = k
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for k in [i...3]
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ii[k] = k+1
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for k in [0...j]
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jj[k] = k
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for k in [0...3]
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jj[k] = k+1
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fac = m[ii[0]][jj[0]] * (m[ii[1]][jj[1]]*m[ii[2]][jj[2]] - m[ii[1]][jj[2]]*m[ii[2]][jj[1]])
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fac -= m[ii[0]][jj[1]] * (m[ii[1]][jj[0]]*m[ii[2]][jj[2]] - m[ii[1]][jj[2]]*m[ii[2]][jj[0]])
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fac += m[ii[0]][jj[2]] * (m[ii[1]][jj[0]]*m[ii[2]][jj[1]] - m[ii[1]][jj[1]]*m[ii[2]][jj[0]])
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k = i+j
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if k != (k/2)*2 # compute sign
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fac = -fac
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fac
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@DETERMINANT_4X4: (m) ->
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d = m[0][0] * @COFACTOR_4X4_IJ m, 0, 0
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d += m[0][1] * @COFACTOR_4X4_IJ m, 0, 1
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d += m[0][2] * @COFACTOR_4X4_IJ m, 0, 2
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d += m[0][3] * @COFACTOR_4X4_IJ m, 0, 3
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d
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@SCALE_ADJOINT_4X4: (a,s,m) ->
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for i in [0...4]
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for j in [0...4]
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a[j][i] = @COFACTOR_4X4_IJ m, i, j
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a[j][i] *= s
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@INVERT_4X4: (b,a) ->
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det = @DETERMINANT_4X4 a
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@SCALE_ADJOINT_4X4 b, 1.0 / det, a
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invert: () ->
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t = [[],[],[],[]]
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inv = [[],[],[],[]]
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t[0][0] = @matrix[0]
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t[0][1] = @matrix[1]
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t[0][2] = @matrix[2]
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t[0][3] = @matrix[3]
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t[1][0] = @matrix[4]
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t[1][1] = @matrix[5]
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t[1][2] = @matrix[6]
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t[1][3] = @matrix[7]
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t[2][0] = @matrix[8]
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t[2][1] = @matrix[9]
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t[2][2] = @matrix[10]
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t[2][3] = @matrix[11]
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t[3][0] = @matrix[12]
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t[3][1] = @matrix[13]
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t[3][2] = @matrix[14]
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t[3][3] = @matrix[15]
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Matrix.INVERT_4X4 inv, t
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@matrix[0] = inv[0][0]
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@matrix[1] = inv[0][1]
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@matrix[2] = inv[0][2]
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@matrix[3] = inv[0][3]
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@matrix[4] = inv[1][0]
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@matrix[5] = inv[1][1]
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@matrix[6] = inv[1][2]
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@matrix[7] = inv[1][3]
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@matrix[8] = inv[2][0]
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@matrix[9] = inv[2][1]
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@matrix[10] = inv[2][2]
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@matrix[11] = inv[2][3]
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@matrix[12] = inv[3][0]
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@matrix[13] = inv[3][1]
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@matrix[14] = inv[3][2]
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@matrix[15] = inv[3][3]
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@
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getQuaternion: () ->
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tr = @matrix[0] + @matrix[5] + @matrix[10]
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if tr > 0.0 # check the diagonal
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s = Math.sqrt tr + 1.0
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ss = 0.5 / s
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new Quaternion s/2.0, (@matrix[6]-@matrix[9])*ss,
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(@matrix[8]-@matrix[2])*ss,
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(@matrix[1]-@matrix[4])*ss
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else # diagonal is negative
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i = 0
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nxt = [1, 2, 0]
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q = [0,0,0,0]
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i = 1 if @matrix[5] > @matrix[0]
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i = 2 if @matrix[10] > @matrix[i*4+i]
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j = nxt[i]
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k = nxt[j]
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s = Math.sqrt (@matrix[i*4+i] - (@matrix[j*4+j] + @matrix[k*4+k])) + 1.0
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q[i] = s * 0.5
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s = 0.5 / s if s != 0.0
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q[3] = (@matrix[j*4+k] - @matrix[k*4+j]) * s
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q[j] = (@matrix[i*4+j] + @matrix[j*4+i]) * s
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q[k] = (@matrix[i*4+k] + @matrix[k*4+i]) * s
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new Quaternion q[3], q[0], q[1], q[2]
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setPosition: (x,y,z) ->
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v = new Vector x,y,z
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@matrix[12] = v.x
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@matrix[13] = v.y
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@matrix[14] = v.z
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setXVector: (v) ->
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@matrix[0] = v.x
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@matrix[1] = v.y
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@matrix[2] = v.z
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setYVector: (v) ->
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@matrix[4] = v.x
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@matrix[5] = v.y
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@matrix[6] = v.z
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setZVector: (v) ->
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@matrix[8] = v.x
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@matrix[9] = v.y
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@matrix[10] = v.z
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getXVector: () -> new Vector @matrix[0], @matrix[1], @matrix[2]
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getYVector: () -> new Vector @matrix[4], @matrix[5], @matrix[6]
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getZVector: () -> new Vector @matrix[8], @matrix[9], @matrix[10]
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getPosition: () -> new Vector @matrix[12], @matrix[13], @matrix[14]
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module.exports = Matrix
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