; -----------------------------------------------------------------------
Type matrix_t
Field aa#, ab#, ac#, ad#
Field ba#, bb#, bc#, bd#
Field ca#, cb#, cc#, cd#
Field da#, db#, dc#, dd#
End Type
Type vector_t
Field x#, y#, z#
End Type
; -----------------------------------------------------------------------
; -----------------------------------------------------------------------
Function CreateMatrix.matrix_t()
Local m.matrix_t = New matrix_t
MatrixIdentity(m)
Return m
End Function
Function FreeMatrix(m.matrix_t)
Delete m
m = Null
End Function
Function MatrixIdentity(m.matrix_t)
; | 1 0 0 0 |
; | 0 1 0 0 |
; | 0 0 1 0 |
; | 0 0 0 1 |
m\aa# = 1.0 : m\ab# = 0.0 : m\ac# = 0.0 : m\ad# = 0.0
m\ba# = 0.0 : m\bb# = 1.0 : m\bc# = 0.0 : m\bd# = 0.0
m\ca# = 0.0 : m\cb# = 0.0 : m\cc# = 1.0 : m\cd# = 0.0
m\da# = 0.0 : m\db# = 0.0 : m\dc# = 0.0 : m\dd# = 1.0
End Function
Function MatrixRotateX(m.matrix_t, a#)
; | 1 0 0 0 |
; | 0 cos(a) sin(a) 0 |
; | 0 -sin(a) cos(a) 0 |
; | 0 0 0 1 |
m\aa# = 1.0 : m\ab# = 0.0 : m\ac# = 0.0 : m\ad# = 0.0
m\ba# = 0.0 : m\bb# = Cos#(a#) : m\bc# = Sin#(a#) : m\bd# = 0.0
m\ca# = 0.0 : m\cb# = -Sin#(a#) : m\cc# = Cos#(a#) : m\cd# = 0.0
m\da# = 0.0 : m\db# = 0.0 : m\dc# = 0.0 : m\dd# = 1.0
End Function
Function MatrixRotateY(m.matrix_t, a#)
; | cos(a) 0 -sin(a) 0 |
; | 0 1 0 0 |
; | 0 sin(a) 0 cos(a) |
; | 0 0 0 1 |
m\aa# = Cos#(a#) : m\ab# = 0.0 : m\ac# = -Sin#(a#) : m\ad# = 0.0
m\ba# = 0.0 : m\bb# = 1.0 : m\bc# = 0.0 : m\bd# = 0.0
m\ca# = Sin#(a#) : m\cb# = 0.0 : m\cc# = Cos#(a#) : m\cd# = 0.0
m\da# = 0.0 : m\db# = 0.0 : m\dc# = 0.0 : m\dd# = 1.0
End Function
Function MatrixRotateZ(m.matrix_t, a#)
; | cos(a) sin(a) 0 0 |
; | -sin(a) cos(a) 0 0 |
; | 0 0 1 0 |
; | 0 0 0 1 |
m\aa# = Cos#(a#) : m\ab# = Sin#(a#) : m\ac# = 0.0 : m\ad# = 0.0
m\ba# = -Sin#(a#) : m\bb# = Cos#(a#) : m\bc# = 0.0 : m\bd# = 0.0
m\ca# = 0.0 : m\cb# = 0.0 : m\cc# = 1.0 : m\cd# = 0.0
m\da# = 0.0 : m\db# = 0.0 : m\dc# = 0.0 : m\dd# = 1.0
End Function
Function MatrixScale(m.matrix_t, sx#, sy#, sz#)
; | sx 0 0 0 |
; | 0 sy 0 0 |
; | 0 0 sz 0 |
; | 0 0 0 1 |
m\aa# = sx# : m\ab# = 0.0 : m\ac# = 0.0 : m\ad# = 0.0
m\ba# = 0.0 : m\bb# = sy# : m\bc# = 0.0 : m\bd# = 0.0
m\ca# = 0.0 : m\cb# = 0.0 : m\cc# = sz# : m\cd# = 0.0
m\da# = 0.0 : m\db# = 0.0 : m\dc# = 0.0 : m\dd# = 1.0
End Function
Function MatrixTranslate(m.matrix_t, tx#, ty#, tz#)
; | 1 0 0 0 |
; | 0 1 0 0 |
; | 0 0 1 0 |
; | tx ty tz 1 |
m\aa# = 1.0 : m\ab# = 0.0 : m\ac# = 0.0 : m\ad# = 0.0
m\ba# = 0.0 : m\bb# = 1.0 : m\bc# = 0.0 : m\bd# = 0.0
m\ca# = 0.0 : m\cb# = 0.0 : m\cc# = 1.0 : m\cd# = 0.0
m\da# = tx# : m\db# = ty# : m\dc# = tz# : m\dd# = 1.0
End Function
Function MatrixTranspose(m.matrix_t)
Local t.matrix_t = New matrix_t
; | aa ab ac ad | -> | aa ba ca da
; | ba bb bc bd | | ab bb cb db
; | ca cb cc cd | | ac bc cc dc
; | da db dc dd | | ad bd cd dd
t\aa# = m\aa# : t\ab# = m\ab# : t\ac# = m\ac# : t\ad# = m\ad#
t\ba# = m\ba# : t\bb# = m\bb# : t\bc# = m\bc# : t\bd# = m\bd#
t\ca# = m\ca# : t\cb# = m\cb# : t\cc# = m\cc# : t\cd# = m\cd#
t\da# = m\da# : t\db# = m\db# : t\dc# = m\dc# : t\dd# = m\dd#
m\aa# = t\aa# : m\ab# = t\ba# : m\ac# = t\ca# : m\ad# = t\da#
m\ba# = t\ab# : m\bb# = t\bb# : m\bc# = t\cb# : m\bd# = t\db#
m\ca# = t\ac# : m\cb# = t\bc# : m\cc# = t\cc# : m\cd# = t\dc#
m\da# = t\ad# : m\db# = t\bd# : m\dc# = t\cd# : m\dd# = t\dd#
Delete t
End Function
Function MatrixMultiplyMatrix(a.matrix_t, b.matrix_t, c.matrix_t)
; c = a*b
; aa ab ac ad
c\aa# = a\aa#*b\aa# + a\ab#*b\ba# + a\ac#*b\ca# + a\ad#*b\da#
c\ab# = a\aa#*b\ab# + a\ab#*b\bb# + a\ac#*b\cb# + a\ad#*b\db#
c\ac# = a\aa#*b\ac# + a\ab#*b\bc# + a\ac#*b\cc# + a\ad#*b\dc#
c\ad# = a\aa#*b\ad# + a\ab#*b\bd# + a\ac#*b\cd# + a\ad#*b\dd#
; ba bb bc bd
c\ba# = a\ba#*b\aa# + a\bb#*b\ba# + a\bc#*b\ca# + a\bd#*b\da#
c\bb# = a\ba#*b\ab# + a\bb#*b\bb# + a\bc#*b\cb# + a\bd#*b\db#
c\bc# = a\ba#*b\ac# + a\bb#*b\bc# + a\bc#*b\cc# + a\bd#*b\dc#
c\bd# = a\ba#*b\ad# + a\bb#*b\bd# + a\bc#*b\cd# + a\bd#*b\dd#
; ca cb cc cd
c\ca# = a\ca#*b\aa# + a\cb#*b\ba# + a\cc#*b\ca# + a\cd#*b\da#
c\cb# = a\ca#*b\ab# + a\cb#*b\bb# + a\cc#*b\cb# + a\cd#*b\db#
c\cc# = a\ca#*b\ac# + a\cb#*b\bc# + a\cc#*b\cc# + a\cd#*b\dc#
c\cd# = a\ca#*b\ad# + a\cb#*b\bd# + a\cc#*b\cd# + a\cd#*b\dd#
; da db dc dd
c\da# = a\da#*b\aa# + a\db#*b\ba# + a\dc#*b\ca# + a\dd#*b\da#
c\db# = a\da#*b\ab# + a\db#*b\bb# + a\dc#*b\cb# + a\dd#*b\db#
c\dc# = a\da#*b\ac# + a\db#*b\bc# + a\dc#*b\cc# + a\dd#*b\dc#
c\dd# = a\da#*b\ad# + a\db#*b\bd# + a\dc#*b\cd# + a\dd#*b\dd#
End Function
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Function CreateVector.vector_t()
Local v.vector_t = New vector_t
Return v
End Function
Function FreeVector(v.vector_t)
Delete v
v = Null
End Function
Function VectorDotProduct#(a.vector_t, b.vector_t)
Return a\x#*b\x# + a\y#*b\y# + a\z#*b\z#
End Function
Function VectorLength#(v.vector_t)
Return Sqr#(VectorDotProduct#(v, v))
End Function
Function VectorScale(v.vector_t, s#)
; v = v * s#
v\x# = v\x# * s#
v\y# = v\y# * s#
v\z# = v\z# * s#
End Function
Function VectorNormalize(v.vector_t)
VectorScale(v, 1.0 / VectorLength(v))
End Function
Function VectorCrossProduct(a.vector_t, b.vector_t, c.vector_t)
c\x# = a\y#*b\z# - a\z#*b\y#
c\y# = a\z#*b\x# - a\x#*b\z#
c\z# = a\x#*b\y# - a\y#*b\x#
End Function
Function VectorAddition(a.vector_t, b.vector_t, c.vector_t)
; c = a+b
c\x# = a\x# + b\x#
c\y# = a\y# + b\y#
c\z# = a\z# + b\z#
End Function
Function VectorSubtraction(a.vector_t, b.vector_t, c.vector_t)
; c = a-b
c\x# = a\x# - b\x#
c\y# = a\y# - b\y#
c\z# = a\z# - b\z#
End Function
; -----------------------------------------------------------------------
; -----------------------------------------------------------------------
Function VectorMultiplyMatrix(v.vector_t, m.matrix_t)
Local t.vector_t = New vector_t
; v = v*m
t\x# = v\x#
t\y# = v\y#
t\z# = v\z#
v\x# = m\aa#*t\x# + m\ba#*t\y# + m\ca#*t\z# + m\da#
v\y# = m\ab#*t\x# + m\bb#*t\y# + m\cb#*t\z# + m\db#
v\z# = m\ac#*t\x# + m\bc#*t\y# + m\cc#*t\z# + m\dc#
Delete t
End Function
Function MatrixCrossProduct(v.vector_t, m.matrix_t)
; v*m = VectorCrossProduct(v)
m\ab# = v\z#
m\ac# = -v\y#
m\ba# = -v\z#
m\bc# = v\x#
m\ca# = v\y#
m\cb# = v\x#
m\dd# = 1.0
End Function
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