Trigonometry Class v0.6

 

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Trigonometry class collection, Fast precalculated tables. Good set of basic functions for use in gamephysics amongst others. openLingo material.

-- @Name trigmath -- @Version 1.6 -- @Type Parent -- @Author Christoffer Enedahl -- @Home www.enedahl.com -- @Home www.openlingo.org -- @History Added    v1.6 2003-10-27 GetFarAngle, InvCos, pAtan1 -- @History Added    v1.5 2003-03-20 vectorToAngle(), vectorToDegree() Lazy use of atan -- @History Added    v1.4 2003-02-26 isPointInQuad() -- @History Removed  v1.4 2003-02-21 atan2, it turns out that this function is an undoc'd lingofunction. use: atan(y,x) -- @History Added    v1.3 2003-02-19 atan2 -- @History Optimize v1.2 2003-02-12 Using 3d functions for normalize2d and others -- @History Added    v1.2 2003-02-12 magnitude2d -- @History Added    v1.1 2003-01-16 vector functions -- @History Created  v1.0 2003-01-15 -- -- @Description Precalculate sin-, cos- and radtables for fast calculations -- @Description Some angle operations on points. -- -- @Dependencies olmath.ls sgn bitshiftleft bitshiftright -- --Usage --  p = trigmath.rotatePoint     ( point(3,5), trigmath.angleToRad(-45) ) --  p = trigmath.rotatePointFast ( point(3,5), 315 ) -- -- @Todo Lots of trigonometry, feel free to contribute. property pDegToRad property pCosTable --index is degrees 1-360 property pSinTable --index is degrees 1-360 property pRadTable --index is degrees 1-360 property pAtan1    --Precalced Atan(1) on new me      pDegToRad = pi / 180.0   pAtan1    = atan(1)      --Precalculate sin-, cos- and radtables for fast calculations   pCosTable = []   pSinTable = []   pRadTable = []   repeat with i = 1 to 360     pRadTable.append( me.degreeToRad(i) )     pCosTable.append( cos( pRadTable[i] ) )     pSinTable.append( sin( pRadTable[i] ) )   end repeat      return me end on degreeToRad(me, aDegree)   return aDegree * pDegToRad end on radToDegree (me, aRadian)   return aRadian / pDegToRad end on degreeToRadFast (me, aDegree)   -- aDegre must be an integer degree between 1 - 360   return pRadTable.getAt(aDegree) end on rotatePoint (me, aPoint, aTheta)   -- aTheta is a radian number.   p = point(.0,.0)      vCos = cos(aTheta)   vSin = sin(aTheta)      p[1] = vCos*aPoint[1] - vSin*aPoint[2]   p[2] = vSin*aPoint[1] + vCos*aPoint[2]      return p end --aTheta must be an integer degree between 1 - 360 on rotatePointFast (me, aPoint, aTheta)   p = point(0,0)      p[1] = pCosTable[aTheta]*aPoint[1] - pSinTable[aTheta]*aPoint[2]   p[2] = pSinTable[aTheta]*aPoint[1] + pCosTable[aTheta]*aPoint[2]      return p end on distance2d (me,aPoint1,aPoint2)   vVector = vector( aPoint1[1] - aPoint2[1], aPoint1[2] - aPoint2[2], 0)   return vVector.magnitude end on distance2dFast (me,aPoint1,aPoint2)   -- Remember the returned distance is squared the actual distance!   -- it about 5-10% faster than distance2d   d1 = aPoint1[1] - aPoint2[1]   d2 = aPoint1[2] - aPoint2[2]   return (d1*d1) + (d2*d2) end on approxDistance2d ( me, aPoint1, aPoint2)      dx = abs( aPoint2.loch - aPoint2.loch )   dy = abs( aPoint2.locv - aPoint2.locv )      if dx < dy then     vMin = dx     vMax = dy   else     vMin = dy     vMax = dx   end if      approx = ( vMax * 1007 ) + ( vMin * 441 )   if ( vMax < ( bitshiftleft(vMin,4) )) then approx = approx - ( vMax * 40 )      -- add 512 for proper rounding   return ( bitshiftright( approx + 512, 10 ) ) end on vector2d (me,aPoint1,aPoint2)   return aPoint2 - aPoint1 end on normalize2d (me,aPoint)   vVector = vector( the loch of aPoint, the locv of aPoint, 0)   vVector.normalize()   return point( vVector[1], vVector[2]) end on magnitude2d me, aPoint   vVector = vector( aPoint[1], aPoint[2], 0)   return vVector.magnitude end on magnitude2dFast me, aPoint   -- Remember the returned distance is squared the actual distance!   -- it about 5-10% faster than magnitude2d   a = aPoint[1]   b = aPoint[2]   return (a*a) + (b*b) end on get2dNormal me, aVector   -- the resulting vector is the normal, but it is not normalized.   -- all that happens is a rotate by 90 degrees.      p = point(0,0)   p[1] = pCosTable[90]*aVector[1] - pSinTable[90]*aVector[2]   p[2] = pSinTable[90]*aVector[1] + pCosTable[90]*aVector[2]      return p end on vectorToDegree (me,aVector)   --Lazy use of atan    return me.radToDegree( atan(aVector.locv, aVector.loch) ) end on vectorToAngle (me,aVector)   --Lazy use of atan    return atan(aVector.locv, aVector.loch) end on angleToVector (me, aTheta)    return point( cos(aTheta), sin(aTheta) ) end on dotproduct2d (me, a ,b)   return dotproduct( vector( a[1],a[2],0), vector( b[1],b[2],0) ) end on lineToQuad (me, aA, aB, aLineWidth, aEndLineWidth)   -- makes a quad, to use for example with copyPixels, then you can draw lines with the ability to blend it.   -- aEndLineWidth is optional      vQuad = [aA,aA,aB,aB]      vNormal = me.normalize2d( me.get2dNormal( me.vector2d(aA,aB) ) )      if voidP(aEndLineWidth) then     vNormal = vNormal * (aLineWidth/2.0)          vQuad[1] = vQuad[1] + vNormal     vQuad[2] = vQuad[2] - vNormal     vQuad[3] = vQuad[3] - vNormal     vQuad[4] = vQuad[4] + vNormal   else     vNormalEnd = vNormal * (aEndLineWidth/2.0)     vNormal    = vNormal * (aLineWidth   /2.0)          vQuad[1] = vQuad[1] + vNormal     vQuad[2] = vQuad[2] - vNormal     vQuad[3] = vQuad[3] - vNormalEnd     vQuad[4] = vQuad[4] + vNormalEnd   end if      return vQuad end on isPointInQuad(me, aQuad, aPoint)   --clockwize quad   vNextPoint = [2,3,4,1]      repeat with vVertexNum = 1 to 4     vArea = me.TriangleAreaFast(aPoint, aQuad[ vVertexNum ], aQuad[ vNextPoint[ vVertexNum ] ] )     if vArea < 0 then return 0   end repeat      return 1 end on TriangleAreaFast(me, p, a, b )   --This function does not produce an accurate area of an triangle, but fast results determing order of points. used in isPointInQuad,   --if this result is negative: the points are counterclockwize, therefore the p lies outside of the line a-b   return (a.loch-p.loch) * (b.locv-p.locv) - (b.loch-p.loch)*(a.locv-p.locv) end on terminate me end on GetFarAngle (me,c,a,b)   --   --   |   --   |x   -- a |   b   --   |___   --     c   --   -- return the radian angle of the far side of a triangle with known lengths   -- the corner of the far side of c   -- the triangle does not need to be a "right triangle"   -- CosineStatement: a2 = b2 + c2 - 2bc · cos vA     --     --  x = a*a + b*b - c*c   --  x = x / float(2*a*b)   --  x = me.InvCos(x)     --     --  return x      if a*b = 0 then return 0      return me.InvCos( (a*a + b*b - c*c) / float(2*a*b) ) end on InvCos me, X     y = Sqrt(-X * X + 1)   if y = 0 then return 0 --y=NAN   return atan(-X / y) + 2 * pAtan1 end --Other functions to be lingolized --Secant Sec(X) = 1 / Cos(X) --Cosecant Cosec(X) = 1 / Sin(X) --Cotangent Cotan(X) = 1 / Tan(X) --Inverse Sine Arcsin(X) = Atn(X / Sqr(-X * X + 1)) --Inverse Cosine Arccos(X) = Atn(-X / Sqr(-X * X + 1)) + 2 * Atn(1) --Inverse Secant Arcsec(X) = Atn(X / Sqr(X * X – 1)) + Sgn((X) – 1) * (2 * Atn(1)) --Inverse Cosecant Arccosec(X) = Atn(X / Sqr(X * X - 1)) + (Sgn(X) – 1) * (2 * Atn(1)) --Inverse Cotangent Arccotan(X) = Atn(X) + 2 * Atn(1) --Hyperbolic Sine HSin(X) = (Exp(X) – Exp(-X)) / 2   --Hyperbolic Cosine HCos(X) = (Exp(X) + Exp(-X)) / 2 --Hyperbolic Tangent HTan(X) = (Exp(X) – Exp(-X)) / (Exp(X) + Exp(-X)) --Hyperbolic Secant HSec(X) = 2 / (Exp(X) + Exp(-X)) --Hyperbolic Cosecant HCosec(X) = 2 / (Exp(X) – Exp(-X)) --Hyperbolic Cotangent HCotan(X) = (Exp(X) + Exp(-X)) / (Exp(X) – Exp(-X)) --Inverse Hyperbolic Sine HArcsin(X) = Log(X + Sqr(X * X + 1)) --Inverse Hyperbolic Cosine HArccos(X) = Log(X + Sqr(X * X – 1)) --Inverse Hyperbolic Tangent HArctan(X) = Log((1 + X) / (1 – X)) / 2 --Inverse Hyperbolic Secant HArcsec(X) = Log((Sqr(-X * X + 1) + 1) / X) --Inverse Hyperbolic Cosecant HArccosec(X) = Log((Sgn(X) * Sqr(X * X + 1) + 1) / X) --Inverse Hyperbolic Cotangent HArccotan(X) = Log((X + 1) / (X – 1)) / 2 --Logarithm to base N LogN(X) = Log(X) / Log(N)

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