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Rem
bbdoc: noddybox.algorithm
EndRem
Module noddybox.algorithm
ModuleInfo "Framework: Various algorithm routines"
ModuleInfo "Copyright: Public Domain"
ModuleInfo "Author: Ian Cowburn"
ModuleInfo "Version: $Revision$"
' $Id$
Strict
Import brl.math
Import brl.linkedlist
Rem
bbdoc: Used to return integer points from algorithms.
EndRem
Type TAlgoPoint
Rem
bbdoc: The X co-ordinate of the point
EndRem
Field x:Int
Rem
bbdoc: The Y co-ordinate of the point
EndRem
Field y:Int
Rem
bbdoc: Create a point.
returns: Newly created point.
about: @x and @y are initialised with the passed parameters.
EndRem
Function Create:TAlgoPoint(x:Int, y:Int)
Local o:TAlgoPoint=New TAlgoPoint
o.x=x
o.y=y
Return o
End Function
End Type
Rem
bbdoc: Used to return double points from algorithms.
EndRem
Type TAlgoPointD
Rem
bbdoc: The X co-ordinate of the point
EndRem
Field x:Double
Rem
bbdoc: The Y co-ordinate of the point
EndRem
Field y:Double
Rem
bbdoc: Create a point.
returns: Newly created point.
about: @x and @y are initialised with the passed parameters.
EndRem
Function Create:TAlgoPointD(x:Double, y:Double)
Local o:TAlgoPointD=New TAlgoPointD
o.x=x
o.y=y
Return o
End Function
End Type
Rem
bbdoc: Used to return 3D points from algorithms.
EndRem
Type TAlgoPoint3D
Rem
bbdoc: The X co-ordinate of the point
EndRem
Field x:Double
Rem
bbdoc: The Y co-ordinate of the point
EndRem
Field y:Double
Rem
bbdoc: The Z co-ordinate of the point
EndRem
Field z:Double
Rem
bbdoc: Create a point.
returns: Newly created point.
about: @x, @y and @z are initialised with the passed parameters.
EndRem
Function Create:TAlgoPoint3D(x:Double, y:Double, z:Double)
Local o:TAlgoPoint3D=New TAlgoPoint3D
o.x=x
o.y=y
o.z=z
Return o
End Function
End Type
Rem
bbdoc: Rotates a point.
returns: The rotated point.
about: @x, @y are rotated around 0,0 by @angle, which is the value in degrees multiplied by ten.
about: To speed things up a simple 3600 element lookup table is used, so @angle <u>must</u> be 0 to 3599 inclusive, or a runtime error will result.
EndRem
Function DoRotate:TAlgoPoint(x:Int, y:Int, angle:Int)
AlgoStatic.Init()
Local dx:Double=x
Local dy:Double=y
Local dco:Double=AlgoStatic.co[angle]
Local dsi:Double=algoStatic.si[angle]
Return TAlgoPoint.Create(dco*dx+(-dsi)*dy,dsi*dx+dco*dy)
End Function
Rem
bbdoc: Rotates a point (double version)
returns: The rotated point.
about: @x, @y are rotated around 0,0 by @angle, which is the value in degrees multiplied by ten.
about: To speed things up a simple 3600 element lookup table is used, so @angle <u>must</u> be 0 to 3599 inclusive, or a runtime error will result.
EndRem
Function DoRotateD:TAlgoPointD(x:Double, y:Double, angle:Int)
AlgoStatic.Init()
Local dco:Double=AlgoStatic.co[angle]
Local dsi:Double=algoStatic.si[angle]
Return TAlgoPointD.Create(dco*x+(-dsi)*y,dsi*x+dco*y)
End Function
Rem
bbdoc: Implements a Bresenham style line.
returns: A list of points making up the line.
about: @px1, @py1, @px2 and @py2 are the end points of the line.
EndRem
Function DoLine:TList(p1x:Int, p1y:Int, p2x:Int, p2y:Int)
Local list:TList=CreateList()
Local f:Int
Local dx:Int
Local dy:Int
Local ix:Int
Local iy:Int
Local incrE:Int
Local incrNE:Int
Local d:Int
Local x:Int
Local y:Int
Local ymode:Int
dx=p2x-p1x
dy=p2y-p1y
ix=Sgn(dx)
iy=Sgn(dy)
dx=Abs(dx)
dy=Abs(dy)
If dy>dx
ymode=True
d=dx*2-dy
incrE=dx*2
incrNE=(dx-dy)*2
Else
ymode=False
d=dy*2-dx
incrE=dy*2
incrNE=(dy-dx)*2
EndIf
x=p1x
y=p1y
list.AddLast(TAlgoPoint.Create(x,y))
If ymode
While y<>p2y
If d<=0
d:+incrE
y:+iy
Else
d:+incrNE
y:+iy
x:+ix
EndIf
list.AddLast(TAlgoPoint.Create(x,y))
Wend
Else
While x<>p2x
If d<=0
d:+incrE
x:+ix
Else
d:+incrNE
y:+iy
x:+ix
EndIf
list.AddLast(TAlgoPoint.Create(x,y))
Wend
EndIf
Return list
End Function
Rem
bbdoc: Returns the points for degrees 0-359 on the described circle.
returns: A list of points making up the circle.
about: @x, @y is the centre of the circle, @r it's radius.
EndRem
Function DoCircle:TAlgoPoint[](x:Int, y:Int, r:Int)
Local p:TAlgoPoint[]=New TAlgoPoint[360]
Local f:Int
AlgoStatic.Init()
For f=0 To 359
p[f]=TAlgoPoint.Create(x+r*AlgoStatic.si[f*10],y+r*AlgoStatic.co[f*10])
Next
Return p
End Function
Rem
bbdoc: Returns the points where a sphere intersects a 3D line.
returns: null if they don't intersect, one point if it intersects as a tangent, two points otherwise.
about: @x1, @y1, @z1, @x2, @y2 and @z2 describe the line. @cx, @cy, @cz and @rad describe the sphere.
about: Leave the Z co-ords as zero to do a 2D check.
EndRem
Function CircleIntersects:TAlgoPoint3D[](x1:Double, y1:Double, z1:Double, x2:Double, y2:Double, z2:Double, cx:Double, cy:Double, cz:Double, rad:Double)
Local a:Double = Square(x2-x1) + Square(y2-y1) + Square(z2-z1)
Local b:Double = 2 * ( (x2-x1)*(x1-cx) + (y2-y1)*(y1-cy) + (z2-z1)*(z1-cz) )
Local c:Double = Square(x1) + Square(y1) + Square(z1) + Square(cx) + Square(cy) + Square(cz) - 2 * ( cx*x1 + cy*y1 + cz*z1 ) - Square(rad)
Local i:Double = b*b-4*a*c
If i<0
Return Null
ElseIf i=1.0
Local m:Double = -b/(2*a)
If m<0.0 Or m>1.0
Return Null
EndIf
Local p:TAlgoPoint3D[]=New TAlgoPoint3D[1]
p[0]=TAlgoPoint3D.Create( x1+m*(x2-x1), y1+m*(y2-y1), z1 + m*(z2-z1))
Return p
Else
Local e:Double = Sqr(Square(b) - 4*a*c)
Local m1:Double = (-b + e) / (2*a)
Local m2:Double = (-b - e) / (2*a)
If (m2<0.0 Or m2>1.0) And (m1<0.0 Or m1>1.0)
Return Null
ElseIf (m1<0.0 Or m1>1.0)
Local p:TAlgoPoint3D[]=New TAlgoPoint3D[1]
p[0]=TAlgoPoint3D.Create( x1+m2*(x2-x1), y1+m2*(y2-y1), z1+m2*(z2-z1))
Return p
ElseIf m2<0.0 Or m2>1.0
Local p:TAlgoPoint3D[]=New TAlgoPoint3D[1]
p[0]=TAlgoPoint3D.Create( x1+m1*(x2-x1), y1+m1*(y2-y1), z1+m1*(z2-z1))
Return p
Else
Local p:TAlgoPoint3D[]=New TAlgoPoint3D[2]
p[0]=TAlgoPoint3D.Create( x1+m1*(x2-x1), y1+m1*(y2-y1), z1+m1*(z2-z1))
p[1]=TAlgoPoint3D.Create( x1+m2*(x2-x1), y1+m2*(y2-y1), z1+m2*(z2-z1))
Return p
EndIf
EndIf
End Function
Private
Type AlgoStatic
Global done:Int=False
Global si:Double[]
Global co:Double[]
Function Init()
If Not done
si=New Double[3600]
co=New Double[3600]
For Local f:Int=0 To 3599
si[f]=Sin(Double(f)/10)
co[f]=Cos(Double(f)/10)
Next
done=True
EndIf
End Function
End Type
Function Square:Double(x:Double)
Return x*x
End Function
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