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3D math functions by Noel Cower
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715
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BlitzBasic 3D
| Category:
Maths/Physics
;#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 s\Width = Width s\Height = Height s\Depth = Depth Return s End Function Function Vector.Vector(X#=0,Y#=0,Z#=0) Local v.Vector = New Vector v\X = X v\Y = Y v\Z = Z Return v End Function Function VectorAdd(a.Vector,b.Vector) a\X =a\X + b\X a\Y =a\Y + b\Y a\Z =a\Z + b\Z End Function Function VectorSubtract(a.Vector,b.Vector) a\X =a\X - b\X a\Y =a\Y - b\Y a\Z =a\Z - b\Z End Function Function VectorSum.Vector(a.Vector,b.Vector) Return Vector(a\X+b\X,a\Y+b\Y,a\Z+b\Z) End Function Function VectorDifference.Vector(a.Vector,b.Vector) Return Vector(a\X-b\X,a\Y-b\Y,a\Z-b\Z) End Function Function VectorMultiply(a.Vector,b.Vector) a\X =a\X * b\X a\Y =a\Y * b\Y a\Z =a\Z * b\Z End Function Function VectorDivide(a.Vector,b.Vector) a\X =a\X / b\X a\Y =a\Y / b\Y a\Z =a\Z / b\Z End Function Function VectorProduct.Vector(a.Vector,b.Vector) Return Vector(a\X*b\X,a\Y*b\Y,a\Z*b\Z) End Function Function VectorQuotient.Vector(a.Vector,b.Vector) Return Vector(a\X/b\X,a\Y/b\Y,a\Z/b\Z) End Function Function VectorCross.Vector(a.Vector,b.Vector) Return Vector( (a\Y*b\Z)-(a\Z*b\Y), (a\Z*b\X)-(a\X*b\Z), (a\X*b\Y)-(a\Y*b\X) ) End Function Function VectorDot#(a.Vector,b.Vector) Return (a\X*b\X) + (a\Y*b\Y) + (a\Z*b\Z) 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) a\X = a\X / m# a\Y = a\Y / m# a\Z = a\Z / m# End Function Function VectorMagnitude#(a.Vector) Return Sqr(a\X*a\X + a\Y*a\Y + a\Z*a\Z) End Function Function VectorScale(a.Vector,b#) a\X = a\X * b# a\Y = a\Y * b# a\Z = a\Z * b# End Function Function VectorSDivide(a.Vector,b#) a\X = a\X / b# a\Y = a\Y / b# a\Z = a\Z / 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 i\Position = Vector(MinX,MinY,-1) i\Size = 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 c\Position = Vector() c\Size = 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 c\Position\x = min[MX]-.1 c\Position\y = min[MY]-.1 c\Position\z = min[MZ]-.1 c\Size\Width = max[MX]-min[MX]+.2 c\Size\height = max[MY]-min[MY]+.2 c\Size\depth = 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 r\Onscreen = 1 r\x = minx r\y = miny r\width = maxx-minx r\height = maxy-miny Return r End Function Function FreeCube(c.Cube) If c = Null Then Return Delete c\Size Delete c\Position Delete c End Function Function PointInCube(x#,y#,z#,c.Cube) Return (x >= c\Position\X And x <= c\Position\X+c\Size\Width And y => c\Position\Y And y <= c\Position\Y+c\Size\Height And z => c\Position\Z And z <= c\Position\Z+c\Size\Depth) 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
Author Comments:
Various functions used in Vein R3; if you dont know what it does, chances are you dont need it.
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