mirror of
https://gitlab.com/freepascal.org/fpc/pas2js.git
synced 2025-04-10 02:07:55 +02:00
316 lines
16 KiB
ObjectPascal
316 lines
16 KiB
ObjectPascal
{$mode objfpc}
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unit Mat4;
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interface
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uses
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BrowserConsole, JS;
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type
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TScalar = double;
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TScalarArray = array of TScalar;
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type
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TMat4 = class
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public
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constructor Identity;
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constructor Translate(const tx,ty,tz: TScalar);
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constructor RotateZ(const Angle:TScalar);
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constructor RotateY(const Angle:TScalar);
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constructor RotateX(const Angle:TScalar);
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constructor Scale (const x, y, z: TScalar);
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constructor Ortho(const Left,Right,Bottom,Top,zNear,zFar:TScalar);
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constructor Perspective(const fovy,Aspect,zNear,zFar:TScalar);
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function Multiply (m: TMat4): TMat4;
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function Inverse: TMat4;
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function CopyList: TScalarArray;
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// property Values[const key:TDictionaryKey]:T read GetValue write SetValue; default;
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procedure Show;
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public
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// TODO: multi dimensional arrays aren't going to work
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// for webgl so replace this with something else
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RawComponents:array[0..3, 0..3] of TScalar;
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end;
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procedure SinCos (angle: TScalar; var sinus: TScalar; var cosinus: TScalar);
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implementation
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const
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PI = 3.14159265359;
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DEG2RAD = PI/180.0;
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//RAD2DEG = 180.0/PI;
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//HalfPI = PI*0.5;
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var
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Matrix4x4Identity: TMat4;
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// TODO: this should be in math
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procedure SinCos (angle: TScalar; var sinus: TScalar; var cosinus: TScalar);
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begin
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sinus := sin(angle);
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cosinus := cos(angle);
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end;
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// NOTE: [][] doesn't typecast to array of syntax so we need this
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function TMat4.CopyList: TScalarArray;
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var
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x, y: integer;
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list: TJSArray;
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begin
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list := TJSArray.new;
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for x := 0 to 3 do
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for y := 0 to 3 do
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list.push(RawComponents[x,y]);
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result := TScalarArray(list);
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end;
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function TMat4.Inverse:TMat4;
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var
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t0,t4,t8,t12,d:TScalar;
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begin
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t0:=(((RawComponents[1,1]*RawComponents[2,2]*RawComponents[3,3])-(RawComponents[1,1]*RawComponents[2,3]*RawComponents[3,2]))-(RawComponents[2,1]*RawComponents[1,2]*RawComponents[3,3])+(RawComponents[2,1]*RawComponents[1,3]*RawComponents[3,2])+(RawComponents[3,1]*RawComponents[1,2]*RawComponents[2,3]))-(RawComponents[3,1]*RawComponents[1,3]*RawComponents[2,2]);
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t4:=((((-(RawComponents[1,0]*RawComponents[2,2]*RawComponents[3,3]))+(RawComponents[1,0]*RawComponents[2,3]*RawComponents[3,2])+(RawComponents[2,0]*RawComponents[1,2]*RawComponents[3,3]))-(RawComponents[2,0]*RawComponents[1,3]*RawComponents[3,2]))-(RawComponents[3,0]*RawComponents[1,2]*RawComponents[2,3]))+(RawComponents[3,0]*RawComponents[1,3]*RawComponents[2,2]);
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t8:=((((RawComponents[1,0]*RawComponents[2,1]*RawComponents[3,3])-(RawComponents[1,0]*RawComponents[2,3]*RawComponents[3,1]))-(RawComponents[2,0]*RawComponents[1,1]*RawComponents[3,3]))+(RawComponents[2,0]*RawComponents[1,3]*RawComponents[3,1])+(RawComponents[3,0]*RawComponents[1,1]*RawComponents[2,3]))-(RawComponents[3,0]*RawComponents[1,3]*RawComponents[2,1]);
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t12:=((((-(RawComponents[1,0]*RawComponents[2,1]*RawComponents[3,2]))+(RawComponents[1,0]*RawComponents[2,2]*RawComponents[3,1])+(RawComponents[2,0]*RawComponents[1,1]*RawComponents[3,2]))-(RawComponents[2,0]*RawComponents[1,2]*RawComponents[3,1]))-(RawComponents[3,0]*RawComponents[1,1]*RawComponents[2,2]))+(RawComponents[3,0]*RawComponents[1,2]*RawComponents[2,1]);
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d:=(RawComponents[0,0]*t0)+(RawComponents[0,1]*t4)+(RawComponents[0,2]*t8)+(RawComponents[0,3]*t12);
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result := TMat4.Identity;
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if d<>0.0 then begin
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d:=1.0/d;
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result.RawComponents[0,0]:=t0*d;
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result.RawComponents[0,1]:=(((((-(RawComponents[0,1]*RawComponents[2,2]*RawComponents[3,3]))+(RawComponents[0,1]*RawComponents[2,3]*RawComponents[3,2])+(RawComponents[2,1]*RawComponents[0,2]*RawComponents[3,3]))-(RawComponents[2,1]*RawComponents[0,3]*RawComponents[3,2]))-(RawComponents[3,1]*RawComponents[0,2]*RawComponents[2,3]))+(RawComponents[3,1]*RawComponents[0,3]*RawComponents[2,2]))*d;
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result.RawComponents[0,2]:=(((((RawComponents[0,1]*RawComponents[1,2]*RawComponents[3,3])-(RawComponents[0,1]*RawComponents[1,3]*RawComponents[3,2]))-(RawComponents[1,1]*RawComponents[0,2]*RawComponents[3,3]))+(RawComponents[1,1]*RawComponents[0,3]*RawComponents[3,2])+(RawComponents[3,1]*RawComponents[0,2]*RawComponents[1,3]))-(RawComponents[3,1]*RawComponents[0,3]*RawComponents[1,2]))*d;
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result.RawComponents[0,3]:=(((((-(RawComponents[0,1]*RawComponents[1,2]*RawComponents[2,3]))+(RawComponents[0,1]*RawComponents[1,3]*RawComponents[2,2])+(RawComponents[1,1]*RawComponents[0,2]*RawComponents[2,3]))-(RawComponents[1,1]*RawComponents[0,3]*RawComponents[2,2]))-(RawComponents[2,1]*RawComponents[0,2]*RawComponents[1,3]))+(RawComponents[2,1]*RawComponents[0,3]*RawComponents[1,2]))*d;
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result.RawComponents[1,0]:=t4*d;
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result.RawComponents[1,1]:=((((RawComponents[0,0]*RawComponents[2,2]*RawComponents[3,3])-(RawComponents[0,0]*RawComponents[2,3]*RawComponents[3,2]))-(RawComponents[2,0]*RawComponents[0,2]*RawComponents[3,3])+(RawComponents[2,0]*RawComponents[0,3]*RawComponents[3,2])+(RawComponents[3,0]*RawComponents[0,2]*RawComponents[2,3]))-(RawComponents[3,0]*RawComponents[0,3]*RawComponents[2,2]))*d;
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result.RawComponents[1,2]:=(((((-(RawComponents[0,0]*RawComponents[1,2]*RawComponents[3,3]))+(RawComponents[0,0]*RawComponents[1,3]*RawComponents[3,2])+(RawComponents[1,0]*RawComponents[0,2]*RawComponents[3,3]))-(RawComponents[1,0]*RawComponents[0,3]*RawComponents[3,2]))-(RawComponents[3,0]*RawComponents[0,2]*RawComponents[1,3]))+(RawComponents[3,0]*RawComponents[0,3]*RawComponents[1,2]))*d;
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result.RawComponents[1,3]:=(((((RawComponents[0,0]*RawComponents[1,2]*RawComponents[2,3])-(RawComponents[0,0]*RawComponents[1,3]*RawComponents[2,2]))-(RawComponents[1,0]*RawComponents[0,2]*RawComponents[2,3]))+(RawComponents[1,0]*RawComponents[0,3]*RawComponents[2,2])+(RawComponents[2,0]*RawComponents[0,2]*RawComponents[1,3]))-(RawComponents[2,0]*RawComponents[0,3]*RawComponents[1,2]))*d;
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result.RawComponents[2,0]:=t8*d;
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result.RawComponents[2,1]:=(((((-(RawComponents[0,0]*RawComponents[2,1]*RawComponents[3,3]))+(RawComponents[0,0]*RawComponents[2,3]*RawComponents[3,1])+(RawComponents[2,0]*RawComponents[0,1]*RawComponents[3,3]))-(RawComponents[2,0]*RawComponents[0,3]*RawComponents[3,1]))-(RawComponents[3,0]*RawComponents[0,1]*RawComponents[2,3]))+(RawComponents[3,0]*RawComponents[0,3]*RawComponents[2,1]))*d;
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result.RawComponents[2,2]:=(((((RawComponents[0,0]*RawComponents[1,1]*RawComponents[3,3])-(RawComponents[0,0]*RawComponents[1,3]*RawComponents[3,1]))-(RawComponents[1,0]*RawComponents[0,1]*RawComponents[3,3]))+(RawComponents[1,0]*RawComponents[0,3]*RawComponents[3,1])+(RawComponents[3,0]*RawComponents[0,1]*RawComponents[1,3]))-(RawComponents[3,0]*RawComponents[0,3]*RawComponents[1,1]))*d;
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result.RawComponents[2,3]:=(((((-(RawComponents[0,0]*RawComponents[1,1]*RawComponents[2,3]))+(RawComponents[0,0]*RawComponents[1,3]*RawComponents[2,1])+(RawComponents[1,0]*RawComponents[0,1]*RawComponents[2,3]))-(RawComponents[1,0]*RawComponents[0,3]*RawComponents[2,1]))-(RawComponents[2,0]*RawComponents[0,1]*RawComponents[1,3]))+(RawComponents[2,0]*RawComponents[0,3]*RawComponents[1,1]))*d;
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result.RawComponents[3,0]:=t12*d;
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result.RawComponents[3,1]:=(((((RawComponents[0,0]*RawComponents[2,1]*RawComponents[3,2])-(RawComponents[0,0]*RawComponents[2,2]*RawComponents[3,1]))-(RawComponents[2,0]*RawComponents[0,1]*RawComponents[3,2]))+(RawComponents[2,0]*RawComponents[0,2]*RawComponents[3,1])+(RawComponents[3,0]*RawComponents[0,1]*RawComponents[2,2]))-(RawComponents[3,0]*RawComponents[0,2]*RawComponents[2,1]))*d;
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result.RawComponents[3,2]:=(((((-(RawComponents[0,0]*RawComponents[1,1]*RawComponents[3,2]))+(RawComponents[0,0]*RawComponents[1,2]*RawComponents[3,1])+(RawComponents[1,0]*RawComponents[0,1]*RawComponents[3,2]))-(RawComponents[1,0]*RawComponents[0,2]*RawComponents[3,1]))-(RawComponents[3,0]*RawComponents[0,1]*RawComponents[1,2]))+(RawComponents[3,0]*RawComponents[0,2]*RawComponents[1,1]))*d;
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result.RawComponents[3,3]:=(((((RawComponents[0,0]*RawComponents[1,1]*RawComponents[2,2])-(RawComponents[0,0]*RawComponents[1,2]*RawComponents[2,1]))-(RawComponents[1,0]*RawComponents[0,1]*RawComponents[2,2]))+(RawComponents[1,0]*RawComponents[0,2]*RawComponents[2,1])+(RawComponents[2,0]*RawComponents[0,1]*RawComponents[1,2]))-(RawComponents[2,0]*RawComponents[0,2]*RawComponents[1,1]))*d;
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end;
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end;
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function TMat4.Multiply (m: TMat4): TMat4;
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begin
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result := TMat4.Identity;
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result.RawComponents[0,0]:=(m.RawComponents[0,0]*self.RawComponents[0,0])+(m.RawComponents[0,1]*self.RawComponents[1,0])+(m.RawComponents[0,2]*self.RawComponents[2,0])+(m.RawComponents[0,3]*self.RawComponents[3,0]);
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result.RawComponents[0,1]:=(m.RawComponents[0,0]*self.RawComponents[0,1])+(m.RawComponents[0,1]*self.RawComponents[1,1])+(m.RawComponents[0,2]*self.RawComponents[2,1])+(m.RawComponents[0,3]*self.RawComponents[3,1]);
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result.RawComponents[0,2]:=(m.RawComponents[0,0]*self.RawComponents[0,2])+(m.RawComponents[0,1]*self.RawComponents[1,2])+(m.RawComponents[0,2]*self.RawComponents[2,2])+(m.RawComponents[0,3]*self.RawComponents[3,2]);
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result.RawComponents[0,3]:=(m.RawComponents[0,0]*self.RawComponents[0,3])+(m.RawComponents[0,1]*self.RawComponents[1,3])+(m.RawComponents[0,2]*self.RawComponents[2,3])+(m.RawComponents[0,3]*self.RawComponents[3,3]);
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result.RawComponents[1,0]:=(m.RawComponents[1,0]*self.RawComponents[0,0])+(m.RawComponents[1,1]*self.RawComponents[1,0])+(m.RawComponents[1,2]*self.RawComponents[2,0])+(m.RawComponents[1,3]*self.RawComponents[3,0]);
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result.RawComponents[1,1]:=(m.RawComponents[1,0]*self.RawComponents[0,1])+(m.RawComponents[1,1]*self.RawComponents[1,1])+(m.RawComponents[1,2]*self.RawComponents[2,1])+(m.RawComponents[1,3]*self.RawComponents[3,1]);
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result.RawComponents[1,2]:=(m.RawComponents[1,0]*self.RawComponents[0,2])+(m.RawComponents[1,1]*self.RawComponents[1,2])+(m.RawComponents[1,2]*self.RawComponents[2,2])+(m.RawComponents[1,3]*self.RawComponents[3,2]);
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result.RawComponents[1,3]:=(m.RawComponents[1,0]*self.RawComponents[0,3])+(m.RawComponents[1,1]*self.RawComponents[1,3])+(m.RawComponents[1,2]*self.RawComponents[2,3])+(m.RawComponents[1,3]*self.RawComponents[3,3]);
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result.RawComponents[2,0]:=(m.RawComponents[2,0]*self.RawComponents[0,0])+(m.RawComponents[2,1]*self.RawComponents[1,0])+(m.RawComponents[2,2]*self.RawComponents[2,0])+(m.RawComponents[2,3]*self.RawComponents[3,0]);
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result.RawComponents[2,1]:=(m.RawComponents[2,0]*self.RawComponents[0,1])+(m.RawComponents[2,1]*self.RawComponents[1,1])+(m.RawComponents[2,2]*self.RawComponents[2,1])+(m.RawComponents[2,3]*self.RawComponents[3,1]);
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result.RawComponents[2,2]:=(m.RawComponents[2,0]*self.RawComponents[0,2])+(m.RawComponents[2,1]*self.RawComponents[1,2])+(m.RawComponents[2,2]*self.RawComponents[2,2])+(m.RawComponents[2,3]*self.RawComponents[3,2]);
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result.RawComponents[2,3]:=(m.RawComponents[2,0]*self.RawComponents[0,3])+(m.RawComponents[2,1]*self.RawComponents[1,3])+(m.RawComponents[2,2]*self.RawComponents[2,3])+(m.RawComponents[2,3]*self.RawComponents[3,3]);
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result.RawComponents[3,0]:=(m.RawComponents[3,0]*self.RawComponents[0,0])+(m.RawComponents[3,1]*self.RawComponents[1,0])+(m.RawComponents[3,2]*self.RawComponents[2,0])+(m.RawComponents[3,3]*self.RawComponents[3,0]);
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result.RawComponents[3,1]:=(m.RawComponents[3,0]*self.RawComponents[0,1])+(m.RawComponents[3,1]*self.RawComponents[1,1])+(m.RawComponents[3,2]*self.RawComponents[2,1])+(m.RawComponents[3,3]*self.RawComponents[3,1]);
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result.RawComponents[3,2]:=(m.RawComponents[3,0]*self.RawComponents[0,2])+(m.RawComponents[3,1]*self.RawComponents[1,2])+(m.RawComponents[3,2]*self.RawComponents[2,2])+(m.RawComponents[3,3]*self.RawComponents[3,2]);
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result.RawComponents[3,3]:=(m.RawComponents[3,0]*self.RawComponents[0,3])+(m.RawComponents[3,1]*self.RawComponents[1,3])+(m.RawComponents[3,2]*self.RawComponents[2,3])+(m.RawComponents[3,3]*self.RawComponents[3,3]);
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end;
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constructor TMat4.Scale (const x, y, z: TScalar);
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begin
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RawComponents[0,0] := x;
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RawComponents[0,1] := 0;
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RawComponents[0,2] := 0;
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RawComponents[0,3] := 0;
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RawComponents[1,0] := 0;
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RawComponents[1,1] := y;
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RawComponents[1,2] := 0;
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RawComponents[1,3] := 0;
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RawComponents[2,0] := 0;
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RawComponents[2,1] := 0;
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RawComponents[2,2] := z;
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RawComponents[2,3] := 0;
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RawComponents[3,0] := 0;
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RawComponents[3,1] := 0;
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RawComponents[3,2] := 0;
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RawComponents[3,3] := 1;
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end;
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constructor TMat4.RotateX(const Angle:TScalar);
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begin
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RawComponents[0,0]:=1.0;
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RawComponents[0,1]:=0.0;
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RawComponents[0,2]:=0.0;
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RawComponents[0,3]:=0.0;
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RawComponents[1,0]:=0.0;
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SinCos(Angle,RawComponents[1,2],RawComponents[1,1]);
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RawComponents[1,3]:=0.0;
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RawComponents[2,0]:=0.0;
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RawComponents[2,1]:=-RawComponents[1,2];
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RawComponents[2,2]:=RawComponents[1,1];
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RawComponents[2,3]:=0.0;
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RawComponents[3,0]:=0.0;
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RawComponents[3,1]:=0.0;
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RawComponents[3,2]:=0.0;
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RawComponents[3,3]:=1.0;
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end;
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constructor TMat4.RotateY(const Angle:TScalar);
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begin
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SinCos(Angle,RawComponents[2,0],RawComponents[0,0]);
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RawComponents[0,1]:=0.0;
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RawComponents[0,2]:=-RawComponents[2,0];
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RawComponents[0,3]:=0.0;
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RawComponents[1,0]:=0.0;
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RawComponents[1,1]:=1.0;
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RawComponents[1,2]:=0.0;
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RawComponents[1,3]:=0.0;
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RawComponents[2,1]:=0.0;
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RawComponents[2,2]:=RawComponents[0,0];
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RawComponents[2,3]:=0.0;
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RawComponents[3,0]:=0.0;
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RawComponents[3,1]:=0.0;
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RawComponents[3,2]:=0.0;
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RawComponents[3,3]:=1.0;
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end;
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constructor TMat4.RotateZ(const Angle:TScalar);
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begin
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SinCos(Angle,RawComponents[0,1],RawComponents[0,0]);
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RawComponents[0,2]:=0.0;
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RawComponents[0,3]:=0.0;
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RawComponents[1,0]:=-RawComponents[0,1];
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RawComponents[1,1]:=RawComponents[0,0];
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RawComponents[1,2]:=0.0;
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RawComponents[1,3]:=0.0;
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RawComponents[2,0]:=0.0;
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RawComponents[2,1]:=0.0;
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RawComponents[2,2]:=1.0;
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RawComponents[2,3]:=0.0;
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RawComponents[3,0]:=0.0;
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RawComponents[3,1]:=0.0;
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RawComponents[3,2]:=0.0;
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RawComponents[3,3]:=1.0;
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end;
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constructor TMat4.Translate(const tx,ty,tz: TScalar);
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begin
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RawComponents[0,0]:=1.0;
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RawComponents[0,1]:=0.0;
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RawComponents[0,2]:=0.0;
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RawComponents[0,3]:=0.0;
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RawComponents[1,0]:=0.0;
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RawComponents[1,1]:=1.0;
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RawComponents[1,2]:=0.0;
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RawComponents[1,3]:=0.0;
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RawComponents[2,0]:=0.0;
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RawComponents[2,1]:=0.0;
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RawComponents[2,2]:=1.0;
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RawComponents[2,3]:=0.0;
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RawComponents[3,0]:=tx;
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RawComponents[3,1]:=ty;
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RawComponents[3,2]:=tz;
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RawComponents[3,3]:=1.0;
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end;
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constructor TMat4.Ortho(const Left,Right,Bottom,Top,zNear,zFar:TScalar);
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var
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rml,tmb,fmn:TScalar;
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begin
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rml:=Right-Left;
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tmb:=Top-Bottom;
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fmn:=zFar-zNear;
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RawComponents[0,0]:=2.0/rml;
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RawComponents[0,1]:=0.0;
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RawComponents[0,2]:=0.0;
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RawComponents[0,3]:=0.0;
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RawComponents[1,0]:=0.0;
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RawComponents[1,1]:=2.0/tmb;
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RawComponents[1,2]:=0.0;
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RawComponents[1,3]:=0.0;
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RawComponents[2,0]:=0.0;
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RawComponents[2,1]:=0.0;
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RawComponents[2,2]:=(-2.0)/fmn;
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RawComponents[2,3]:=0.0;
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RawComponents[3,0]:=(-(Right+Left))/rml;
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RawComponents[3,1]:=(-(Top+Bottom))/tmb;
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RawComponents[3,2]:=(-(zFar+zNear))/fmn;
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RawComponents[3,3]:=1.0;
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end;
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constructor TMat4.Perspective(const fovy,Aspect,zNear,zFar:TScalar);
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var
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Sine,Cotangent,ZDelta,Radians:TScalar;
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begin
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Radians:=(fovy*0.5)*DEG2RAD;
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ZDelta:=zFar-zNear;
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Sine:=sin(Radians);
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if not ((ZDelta=0) or (Sine=0) or (aspect=0)) then begin
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Cotangent:=cos(Radians)/Sine;
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// NOTE: What happens on copy?
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RawComponents:=Matrix4x4Identity.RawComponents;
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RawComponents[0,0]:=Cotangent/aspect;
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RawComponents[1,1]:=Cotangent;
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RawComponents[2,2]:=(-(zFar+zNear))/ZDelta;
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RawComponents[2,3]:=-1-0;
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RawComponents[3,2]:=(-(2.0*zNear*zFar))/ZDelta;
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RawComponents[3,3]:=0.0;
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end;
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end;
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constructor TMat4.Identity;
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begin
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RawComponents[0,0]:=1.0;
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RawComponents[0,1]:=0.0;
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RawComponents[0,2]:=0.0;
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RawComponents[0,3]:=0.0;
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RawComponents[1,0]:=0.0;
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RawComponents[1,1]:=1.0;
|
|
RawComponents[1,2]:=0.0;
|
|
RawComponents[1,3]:=0.0;
|
|
|
|
RawComponents[2,0]:=0.0;
|
|
RawComponents[2,1]:=0.0;
|
|
RawComponents[2,2]:=1.0;
|
|
RawComponents[2,3]:=0.0;
|
|
|
|
RawComponents[3,0]:=0.0;
|
|
RawComponents[3,1]:=0.0;
|
|
RawComponents[3,2]:=0.0;
|
|
RawComponents[3,3]:=1.0;
|
|
end;
|
|
|
|
procedure TMat4.Show;
|
|
var
|
|
x, y: integer;
|
|
begin
|
|
for y := 0 to 3 do
|
|
begin
|
|
write('[');
|
|
for x := 0 to 3 do
|
|
begin
|
|
if x < 3 then
|
|
write(RawComponents[x, y], ',')
|
|
else
|
|
write(RawComponents[x, y]);
|
|
end;
|
|
write(']');
|
|
end;
|
|
end;
|
|
|
|
begin
|
|
Matrix4x4Identity := TMat4.Identity;
|
|
end.
|