[bb] 3D math functions by N [ 1+ years ago ]

[BlitzBot]

Title : 3D math functions
Author : N
Posted : 1+ years ago

Description : Various functions used in Vein R3; if you don't know what it does, chances are you don't need it.

Code :

Code (blitzbasic) Select Expand

;#Region DESCRIPTION
;; Math functions, Vector class taken from the Anima engine (written by me)
;#End Region

;#Region CLASSES
Type Vector
Field X#
Field Y#
Field Z#
End Type

Type Size
Field Width#
Field Height#
Field Depth#
End Type

Type Cube
Field Position.Vector
Field Size.Size
End Type

Type Rectangle
Field X,Y,Width,Height
Field Onscreen
End Type
;#End Region

;#Region PROCEDURES
Function Size.Size(Width#=0,Height#=0,Depth#=0)
Local s.Size = New Size
sWidth = Width
sHeight = Height
sDepth = Depth
Return s
End Function

Function Vector.Vector(X#=0,Y#=0,Z#=0)
Local v.Vector = New Vector
vX = X
vY = Y
v = Z
Return v
End Function

Function VectorAdd(a.Vector,b.Vector)
aX =aX + bX
aY =aY + bY
a =a + b
End Function

Function VectorSubtract(a.Vector,b.Vector)
aX =aX - bX
aY =aY - bY
a =a - b
End Function

Function VectorSum.Vector(a.Vector,b.Vector)
Return Vector(aX+bX,aY+bY,a+b)
End Function

Function VectorDifference.Vector(a.Vector,b.Vector)
Return Vector(aX-bX,aY-bY,a-b)
End Function

Function VectorMultiply(a.Vector,b.Vector)
aX =aX * bX
aY =aY * bY
a =a * b
End Function

Function VectorDivide(a.Vector,b.Vector)
aX =aX / bX
aY =aY / bY
a =a / b
End Function

Function VectorProduct.Vector(a.Vector,b.Vector)
Return Vector(aX*bX,aY*bY,a*b)
End Function

Function VectorQuotient.Vector(a.Vector,b.Vector)
Return Vector(aX/bX,aY/bY,a/b)
End Function

Function VectorCross.Vector(a.Vector,b.Vector)
Return Vector( (aY*b)-(a*bY), (a*bX)-(aX*b), (aX*bY)-(aY*bX) )
End Function

Function VectorDot#(a.Vector,b.Vector)
Return (aX*bX) + (aY*bY) + (a*b)
End Function

Function VectorAngle#(a.Vector,b.Vector)
Local d# = VectorDot(a,b)
Local m# = VectorMagnitude(a)*VectorMagnitude(b)
Return ACos(d#/m#)
End Function

Function VectorNormalize(a.Vector)
Local m# = VectorMagnitude(a)
aX = aX / m#
aY = aY / m#
a = a / m#
End Function

Function VectorMagnitude#(a.Vector)
Return Sqr(aX*aX + aY*aY + a*a)
End Function

Function VectorScale(a.Vector,b#)
aX = aX * b#
aY = aY * b#
a = a * b#
End Function

Function VectorSDivide(a.Vector,b#)
aX = aX / b#
aY = aY / b#
a = a / b#
End Function

Function MinF#(A#,B#)
If A < B Then Return B
Return A
End Function

Function MinI%(A%,B%)
If A < B Then Return B
Return A
End Function

Function MaxF#(A#,B#)
If A > B Then Return B
Return A
End Function

Function MaxI%(A%,B%)
If A > B Then Return B
Return A
End Function

Function ConstrictF#(A#,B#,C#)
If A > C Then
While A > C
A = A - (C-B)
Wend
ElseIf A < B Then
While A < B
A = A + (C-B)
Wend
EndIf
Return A
End Function

Function ConstrictI#(A%,B%,C%)
If A > C Then
While A > C
A = A - (C-B)
Wend
ElseIf A < B Then
While A < B
A = A + (C-B)
Wend
EndIf
Return A
End Function

Function PointInRect(PX,PY,RX,RY,W,H)
Return (PX >= RX) And (PY >= RY) And (PX <= RX+W) And (PY <= RY+H)
End Function

Function NearestPower(N#)
v# = 1
While N# > v#
v# = v# * 2
Wend
k# = v# - N#
Return v/(1 Or (k# > v/4))
End Function

Function GetCube.Cube(Camera,x#,y#,z#,sx#,sy#,sz#)
Local MinX=9999,MinY=9999,MaxX=-9999,MaxY=-9999,MaxZ=-9999

Local c = Camera

CameraProject c,x,y,z
px = ProjectedX()
py = ProjectedY()
pz = ProjectedZ()

If px < MinX Then MinX = px
If py < MinY Then MinY = py
If px > MaxX Then MaxX = px
If py > MaxY Then MaxY = py
If pz > MaxZ Then MaxZ = pz

CameraProject c,sx,y,z
px = ProjectedX()
py = ProjectedY()
pz = ProjectedZ()

If px < MinX Then MinX = px
If py < MinY Then MinY = py
If px > MaxX Then MaxX = px
If py > MaxY Then MaxY = py
If pz > MaxZ Then MaxZ = pz

CameraProject c,sx,y,sz
px = ProjectedX()
py = ProjectedY()
pz = ProjectedZ()

If px < MinX Then MinX = px
If py < MinY Then MinY = py
If px > MaxX Then MaxX = px
If py > MaxY Then MaxY = py
If pz > MaxZ Then MaxZ = pz

CameraProject c,x,y,sz
px = ProjectedX()
py = ProjectedY()
pz = ProjectedZ()

If px < MinX Then MinX = px
If py < MinY Then MinY = py
If px > MaxX Then MaxX = px
If py > MaxY Then MaxY = py
If pz > MaxZ Then MaxZ = pz

CameraProject c,x,sy,z
px = ProjectedX()
py = ProjectedY()
pz = ProjectedZ()

If px < MinX Then MinX = px
If py < MinY Then MinY = py
If px > MaxX Then MaxX = px
If py > MaxY Then MaxY = py
If pz > MaxZ Then MaxZ = pz

CameraProject c,sx,sy,z
px = ProjectedX()
py = ProjectedY()
pz = ProjectedZ()

If px < MinX Then MinX = px
If py < MinY Then MinY = py
If px > MaxX Then MaxX = px
If py > MaxY Then MaxY = py
If pz > MaxZ Then MaxZ = pz

CameraProject c,sx,sy,sz
px = ProjectedX()
py = ProjectedY()
pz = ProjectedZ()

If px < MinX Then MinX = px
If py < MinY Then MinY = py
If px > MaxX Then MaxX = px
If py > MaxY Then MaxY = py
If pz > MaxZ Then MaxZ = pz

CameraProject c,x,sy,sz
px = ProjectedX()
py = ProjectedY()
pz = ProjectedZ()

If px < MinX Then MinX = px
If py < MinY Then MinY = py
If px > MaxX Then MaxX = px
If py > MaxY Then MaxY = py
If pz > MaxZ Then MaxZ = pz

i.Cube = New Cube
iPosition = Vector(MinX,MinY,-1)
iSize = Size(MaxX-MinX,MaxY-MinY,MaxZ)
Return i
End Function

Function CubeInCamera(Camera,x#,y#,z#,sx#,sy#,sz#)
Local c = Camera
Local MinX=9999,MinY=9999,MaxX=-9999,MaxY=-9999

CameraProject c,x,y,z
px = ProjectedX()
py = ProjectedY()
If ProjectedZ() >= 1 Then
If px < MinX Then MinX = px
If px > MaxX Then MaxX = px
If py < MinY Then MinY = py
If py > MaxY Then MaxY = py
EndIf
z = z + ProjectedZ()

CameraProject c,sx,y,z
px = ProjectedX()
py = ProjectedY()
If ProjectedZ() >= 1 Then
If px < MinX Then MinX = px
If px > MaxX Then MaxX = px
If py < MinY Then MinY = py
If py > MaxY Then MaxY = py
EndIf
z = z + ProjectedZ()

CameraProject c,sx,y,sz
px = ProjectedX()
py = ProjectedY()
If ProjectedZ() >= 1 Then
If px < MinX Then MinX = px
If px > MaxX Then MaxX = px
If py < MinY Then MinY = py
If py > MaxY Then MaxY = py
EndIf
z = z + ProjectedZ()

CameraProject c,x,y,sz
px = ProjectedX()
py = ProjectedY()
If ProjectedZ() >= 1 Then
If px < MinX Then MinX = px
If px > MaxX Then MaxX = px
If py < MinY Then MinY = py
If py > MaxY Then MaxY = py
EndIf
z = z + ProjectedZ()

CameraProject c,x,sy,z
px = ProjectedX()
py = ProjectedY()
If ProjectedZ() >= 1 Then
If px < MinX Then MinX = px
If px > MaxX Then MaxX = px
If py < MinY Then MinY = py
If py > MaxY Then MaxY = py
EndIf
z = z + ProjectedZ()

CameraProject c,sx,sy,z
px = ProjectedX()
py = ProjectedY()
If ProjectedZ() >= 1 Then
If px < MinX Then MinX = px
If px > MaxX Then MaxX = px
If py < MinY Then MinY = py
If py > MaxY Then MaxY = py
EndIf
z = z + ProjectedZ()

CameraProject c,sx,sy,sz
px = ProjectedX()
py = ProjectedY()
If ProjectedZ() >= 1 Then
If px < MinX Then MinX = px
If px > MaxX Then MaxX = px
If py < MinY Then MinY = py
If py > MaxY Then MaxY = py
EndIf
z = z + ProjectedZ()

CameraProject c,x,sy,sz
px = ProjectedX()
py = ProjectedY()
If ProjectedZ() >= 1 Then
If px < MinX Then MinX = px
If px > MaxX Then MaxX = px
If py < MinY Then MinY = py
If py > MaxY Then MaxY = py
EndIf
z = z + ProjectedZ()
Stop
If z <= 0 Then Return

Return RectsOverlap(0,0,GraphicsWidth(),GraphicsHeight(),MinX,MinY,maxx-minx,maxy-miny)
End Function

Function GetMeshAABB.Cube(Mesh,glbl=1)
c.Cube = New Cube
cPosition = Vector()
cSize = Size()

Local min#[3]
Local max#[3]

For x# = 0 To 3
min[x] = 65536
max[x] = -65536
Next

Local MX = 1
Local MY = 2
Local MZ = 3

For surfaces = 1 To CountSurfaces(Mesh)
s = GetSurface(Mesh,surfaces)
For i = 0 To CountVertices(s)-1
x# = VertexX(s,i)
y# = VertexY(s,i)
z# = VertexZ(s,i)

If glbl Then
TFormPoint x,y,z,Mesh,0
x = TFormedX()
y = TFormedY()
z = TFormedZ()
EndIf

If x < min[MX] Then min[MX] = x
If x > max[MX] Then max[MX] = x

If y < min[MY] Then min[MY] = y
If y > max[MY] Then max[MY] = y

If z < min[MZ] Then min[MZ] = z
If z > max[MZ] Then max[MZ] = z
Next
Next

cPositionx = min[MX]-.1
cPositiony = min[MY]-.1
cPositionz = min[MZ]-.1
cSizeWidth = max[MX]-min[MX]+.2
cSizeheight = max[MY]-min[MY]+.2
cSizedepth = max[MZ]-min[MZ]+.2
Return c
End Function

Function AABBToScreen.Rectangle(Camera,x#,y#,z#,width#,height#,depth#)
r.Rectangle = New Rectangle

Local minx=16777215,miny=16777215,maxx=-16777215,maxy=-16777215

CameraProject Camera,x,y,z
zs = zs + (ProjectedZ() > 0)
px = ProjectedX()
py = ProjectedY()

If px > maxx Then maxx = px
If px < minx Then minx = px

If py > maxy Then maxy = py
If py < miny Then miny = py

CameraProject Camera,x+width,y,z
zs = zs + (ProjectedZ() > 0)
px = ProjectedX()
py = ProjectedY()

If px > maxx Then maxx = px
If px < minx Then minx = px

If py > maxy Then maxy = py
If py < miny Then miny = py

CameraProject Camera,x+width,y,z+depth
zs = zs + (ProjectedZ() > 0)
px = ProjectedX()
py = ProjectedY()

If px > maxx Then maxx = px
If px < minx Then minx = px

If py > maxy Then maxy = py
If py < miny Then miny = py

CameraProject Camera,x,y,z+depth
zs = zs + (ProjectedZ() > 0)
px = ProjectedX()
py = ProjectedY()

If px > maxx Then maxx = px
If px < minx Then minx = px

If py > maxy Then maxy = py
If py < miny Then miny = py

CameraProject Camera,x,y+height,z
zs = zs + (ProjectedZ() > 0)
px = ProjectedX()
py = ProjectedY()

If px > maxx Then maxx = px
If px < minx Then minx = px

If py > maxy Then maxy = py
If py < miny Then miny = py

CameraProject Camera,x+width,y+height,z
zs = zs + (ProjectedZ() > 0)
px = ProjectedX()
py = ProjectedY()

If px > maxx Then maxx = px
If px < minx Then minx = px

If py > maxy Then maxy = py
If py < miny Then miny = py

CameraProject Camera,x+width,y+height,z+depth
zs = zs + (ProjectedZ() > 0)
px = ProjectedX()
py = ProjectedY()

If px > maxx Then maxx = px
If px < minx Then minx = px

If py > maxy Then maxy = py
If py < miny Then miny = py

CameraProject Camera,x,y+height,z+depth
zs = zs + (ProjectedZ() > 0)
px = ProjectedX()
py = ProjectedY()

If px > maxx Then maxx = px
If px < minx Then minx = px

If py > maxy Then maxy = py
If py < miny Then miny = py

rOnscreen = 1
rx = minx
ry = miny
rwidth = maxx-minx
rheight = maxy-miny

Return r
End Function

Function FreeCube(c.Cube)
If c = Null Then Return
Delete cSize
Delete cPosition
Delete c
End Function

Function PointInCube(x#,y#,z#,c.Cube)
Return (x >= cPositionX And x <= cPositionX+cSizeWidth And y => cPositionY And y <= cPositionY+cSizeHeight And z => cPosition And z <= cPosition+cSizeDepth)
End Function

Function CreateMeshBox(Entity)
Local MinX#,MinY#,MinZ#
Local MaxX#,MaxY#,MaxZ#
For n = 1 To CountSurfaces(Entity)
s = GetSurface(Entity,n)
For i = 0 To CountVertices(s)-1
x# = VertexX(s,i)
y# = VertexY(s,i)
z# = VertexZ(s,i)

If x < MinX Then MinX = x
If x > MaxX Then MaxX = x

If y < MinY Then MinY = y
If y > MaxY Then MaxY = y

If z < MinZ Then MinZ = z
If z > MaxZ Then MaxZ = z
Next
Next
EntityBox Entity,MaxX,MaxY,MaxZ,MinX-MaxX,MinY-MaxY,MinZ-MaxZ
End Function
;#End Region

Comments : none...