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BMax Math Lib v3.0 by Chroma
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BlitzMax
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Maths/Physics
' BMax Math Lib v3.0 ' by Chroma ' Internal Math Vars - Do Not Alter Const Tol:Float = 0.0001 Global vTmp:TVector3 = New TVector3 Global qTmp:TQuaternion = New TQuaternion ' ---------- ' ---------- ' ---------- ' Vector Class Type TVector3 Field x:Double, y:Double, z:Double ' ---------- 'Example1: v1:TVector3 = TVector3.Create(1,2,3) Function Create:TVector3(x:Double = 0, y:Double = 0, z:Double = 0) Local v:TVector3 = New TVector3 v.x = x v.y = y v.z = z Return v End Function 'Example1: v.Set(1,2,3) Method Set(x:Double = 0, y:Double = 0, z:Double = 0) self.x = x self.y = y self.z = z End Method ' ---------- 'Example: v1 = v1 + v2 is written v1.Add( v1, v2 ) Method Add(a:TVector3, b:TVector3) self.x = a.x + b.x self.y = a.y + b.y self.z = a.z + b.z End Method 'Example: v1 = v2 + 5 is written v1.AddScalar( v2, 5 ) Method AddScalar(a:TVector3, s:Double) self.x = a.x + s self.y = a.y + s self.z = a.z + s End Method ' ---------- 'Example: v1 = v2 - v3 is written v1.Sub( v2, v3 ) Method Sub(a:TVector3, b:TVector3) self.x = a.x - b.x self.y = a.y - b.y self.z = a.z - b.z End Method 'Example: v1 = v2 - 5 is written v1.SubScalar( v2, 5 ) Method SubScalar(a:TVector3, s:Double) self.x = a.x - s self.y = a.y - s self.z = a.z - s End Method ' ---------- 'Example: v1 = v2 * v3 is written v1.Mul( v2, v3 ) Method Mul(a:TVector3, b:TVector3) self.x = a.x * b.x self.y = a.y * b.y self.z = a.z * b.z End Method 'Example: v1 = v2 * 5 is written v1.MulScalar( v2, 5 ) Method MulScalar(a:TVector3, s:Double) self.x = a.x * s self.y = a.y * s self.z = a.z * s End Method ' ---------- 'Example: v1 = v2 / v3 is written v1.Div( v2, v3 ) Method Div(a:TVector3, b:TVector3) self.x = a.x / b.x self.y = a.y / b.y self.z = a.z / b.z End Method 'Example: v1 = v2 / 5 is written v1.DivScalar( v2, 5 ) Method DivScalar(a:TVector3, s:Double) self.x = a.x / s self.y = a.y / s self.z = a.z / s End Method ' ---------- 'Example: mag:Double = v.Magnitude() Method Magnitude:Double() Return Sqr(self.x * self.x + self.y * self.y + self.z * self.z) End Method 'Example: v.Normalize() Method Normalize() Local mag:Double = self.Magnitude() self.x :/ mag self.y :/ mag self.z :/ mag If Abs(self.x) < Tol self.x = 0 If Abs(self.y) < Tol self.y = 0 If Abs(self.z) < Tol self.z = 0 End Method ' ---------- 'Example: v1 = v2 ^ v3 is written v1.CrossProduct( v2, v3 ) Method CrossProduct(a:TVector3, b:TVector3) self.x = a.y * b.z - a.z * b.y self.y = -a.x * b.z + a.z * b.x self.z = a.x * b.y - a.y * b.x EndMethod 'Example1: dotp:double = v1.DotProduct( v2 ) Method DotProduct:Double( a:TVector3 ) Return self.x * a.x + self.y * a.y + self.z * a.z End Method ' ---------- 'Returns Inverse Instance of a Vector Method Inverse:TVector3() vTmp.x = -self.x vTmp.y = -self.y vTmp.z = -self.z Return vTmp End Method ' Example: v.GetVecFromQuat( q ) Method GetVecFromQuat(a:TQuaternion) self.x = a.x self.y = a.y self.z = a.z End Method 'Example: v.MakeEulerFromQuat( q ) Method MakeEulerFromQuat(q:TQuaternion) Local r11#, r21#, r31#, r32#, r33#, r12#, r13# Local q00#, q11#, q22#, q33# Local tmp# q00 = q.n * q.n q11 = q.x * q.x q22 = q.y * q.y q33 = q.z * q.z r11 = q00 + q11 - q22 - q33 r21 = 2 * (q.x*q.y + q.n*q.z) r31 = 2 * (q.x*q.z - q.n*q.y) r32 = 2 * (q.y*q.z + q.n*q.x) r33 = q00 - q11 - q22 + q33 tmp = Abs(r31) If (tmp > 0.999999) r12 = 2 * (q.x*q.y - q.n*q.z) r13 = 2 * (q.x*q.z + q.n*q.y) self.x = RadiansToDegrees(0.0) ' roll self.y = RadiansToDegrees( Float (-(Pi/2) * r31/tmp)) ' pitch self.z = RadiansToDegrees( Float ATan2(-r12, -r31*r13))' yaw Else self.x = RadiansToDegrees( Float ATan2(r32, r33)) ' roll self.y = RadiansToDegrees( Float ASin(-r31)) ' pitch self.z = RadiansToDegrees( Float ATan2(r21, r11)) ' yaw EndIf End Method ' ---------- 'Example: vPos.AddTimeStep( vVel, dt ) Method AddTimeStep(a:TVector3, timestep:Float) self.x :+ a.x * timestep self.y :+ a.y * timestep self.z :+ a.z * timestep End Method 'Example: vVel.AddGravity( , dt ) Method AddGravity(g:Float = 9.8, timestep:Float) self.y :- g * timestep End Method 'Example1: v.Show("v",5,5) Method Show(cap:String, xpos:Int, ypos:Int, spc:Int = 12) DrawText cap + "_x:" + self.x,xpos,ypos DrawText cap + "_y:" + self.y,xpos,ypos + spc DrawText cap + "_z:" + self.z,xpos,ypos + spc * 2 End Method End Type ' ---------- ' ---------- ' ---------- ' Quaternion Class Type TQuaternion Field n:Double, x:Double, y:Double, z:Double ' ---------- Function Create:TQuaternion(n:Double = 1.0, x:Double = 0, y:Double = 0, z:Double = 0) Local q:TQuaternion = New TQuaternion q.n = n q.x = x q.y = y q.z = z Return q End Function ' ---------- ' Example: q1=q2+q3 would be q1.Add( q2, q3 ) Method Add(a:TQuaternion, b:TQuaternion) self.n = a.n + b.n self.x = a.x + b.x self.y = a.y + b.y self.z = a.z + b.z End Method ' ---------- ' Example: q1=q2-q3 would be q1.Sub( q2, q3 ) Method Sub(a:TQuaternion, b:TQuaternion) self.n = a.n - b.n self.x = a.x - b.x self.y = a.y - b.y self.z = a.z - b.z End Method ' ---------- ' Example: q1=q2*q3 would be q1.Mul( q2, q3 ) Method Mul(a:TQuaternion, b:TQuaternion) self.n = a.n * b.n - a.x * b.x - a.y * b.y - a.z * b.z self.x = a.n * b.x + a.x * b.n + a.y * b.z - a.z * b.y self.y = a.n * b.y + a.y * b.n + a.z * b.x - a.x * b.z self.z = a.n * b.y + a.y * b.n + a.z * b.x - a.x * b.z End Method ' Example: q1=q2*2 would be q1.MulScalar( q2, 2 ) Method MulScalar( a:TQuaternion, s:Double ) self.n = a.n * s self.x = a.x * s self.y = a.y * s self.z = a.z * s End Method ' ---------- ' Example: q1=q2/2 would be q1.DivS( q2, 2 ) Method DivScalar(a:TQuaternion, s:Double ) self.n = a.n / s self.x = a.x / s self.y = a.y / s self.z = a.z / s End Method ' ---------- ' Example: Local qmag:Double = q.Magnitude() Method Magnitude:Double( a:TQuaternion ) Return Sqr( a.n * a.n + a.x * a.x + a.y * a.y + a.z * a.z ) End Method ' ---------- 'Returns Inverse Instance of a Quaternion Method Inverse:TQuaternion() qTmp.n = self.n qTmp.x = -self.x qTmp.y = -self.y qTmp.z = -self.z Return qTmp End Method ' ---------- 'Example: q.MakeQuatFromEuler( pitch, yaw, roll ) Method MakeQuatFromEuler(x:Float, y:Float, z:Float) Local roll:Float = DegreesToRadians(x) Local pitch:Float = DegreesToRadians(y) Local yaw:Float = DegreesToRadians(z) Local cyaw#, cpitch#, croll#, syaw#, spitch#, sroll# Local cyawcpitch#, syawspitch#, cyawspitch#, syawcpitch# cyaw = Cos(0.5 * yaw) cpitch = Cos(0.5 * pitch) croll = Cos(0.5 * roll) syaw = Sin(0.5 * yaw) spitch = Sin(0.5 * pitch) sroll = Sin(0.5 * roll) cyawcpitch = cyaw*cpitch syawspitch = syaw*spitch cyawspitch = cyaw*spitch syawcpitch = syaw*cpitch self.n = Float (cyawcpitch * croll + syawspitch * sroll) self.x = Float (cyawcpitch * sroll - syawspitch * croll) self.y = Float (cyawspitch * croll + syawcpitch * sroll) self.z = Float (syawcpitch * croll - cyawspitch * sroll) End Method ' ---------- Method Show(cap:String = "", xpos:Int, ypos:Int, spc:Int = 12) DrawText cap + "_w:" + self.n,xpos,ypos DrawText cap + "_x:" + self.x,xpos,ypos + spc DrawText cap + "_y:" + self.y,xpos,ypos + spc * 2 DrawText cap + "_z:" + self.z,xpos,ypos + spc * 3 End Method End Type ' ---------- ' ---------- ' ---------- ' Matrix Class Type TMatrix Field e11:Double, e12:Double, e13:Double Field e21:Double, e22:Double, e23:Double Field e31:Double, e32:Double, e33:Double ' ---------- Function Create:TMatrix(e11!=0, e12!=0, e13!=0, e21!=0, e22!=0, e23!=0, e31!=0, e32!=0, e33!=0) Local m:TMatrix = New TMatrix m.e11 = e11 m.e12 = e12 m.e13 = e13 m.e21 = e21 m.e22 = e22 m.e23 = e23 m.e31 = e31 m.e32 = e32 m.e33 = e33 Return m End Function ' ---------- ' ---------- End Type ' ---------- ' ---------- ' ---------- ' Degrees To Radians Conversion Function DegreesToRadians:Float(deg:Float) Return deg * Pi / 180.0 End Function ' Radians To Degrees Conversion Function RadiansToDegrees:Float(rad:Float) Return rad * 180.0 / Pi End Function
Author Comments:
This math lib is a drastic speed increase over previous libs. Ive done extensive speed testing in massive loops and went with the fastest method every time. Creating and returning a local type inside a method is very inefficient and slow. I gained about a 60-100% speed increase by eliminating it. Give this math lib a shot, youll notice the difference.
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