tasks a-s

Task/Quaternion-type/Delphi/quaternion-type-1.delphi

@@ -0,0 +1,129 @@
+unit Quaternions;
+
+interface
+
+type
+
+  TQuaternion = record
+    A, B, C, D: double;
+
+    function  Init          (aA, aB, aC, aD : double): TQuaternion;
+    function  Norm          : double;
+    function  Conjugate     : TQuaternion;
+    function  ToString      : string;
+
+    class operator Negative (Left : TQuaternion): TQuaternion;
+    class operator Positive (Left : TQuaternion): TQuaternion;
+    class operator Add      (Left, Right : TQuaternion): TQuaternion;
+    class operator Add      (Left : TQuaternion; Right : double): TQuaternion; overload;
+    class operator Add      (Left : double; Right : TQuaternion): TQuaternion; overload;
+    class operator Subtract (Left, Right : TQuaternion): TQuaternion;
+    class operator Multiply (Left, Right : TQuaternion): TQuaternion;
+    class operator Multiply (Left : TQuaternion; Right : double): TQuaternion; overload;
+    class operator Multiply (Left : double; Right : TQuaternion): TQuaternion; overload;
+  end;
+
+implementation
+
+uses
+  SysUtils;
+
+{ TQuaternion }
+
+function TQuaternion.Init(aA, aB, aC, aD: double): TQuaternion;
+begin
+  A := aA;
+  B := aB;
+  C := aC;
+  D := aD;
+
+  result := Self;
+end;
+
+function TQuaternion.Norm: double;
+begin
+  result := sqrt(sqr(A) + sqr(B) + sqr(C) + sqr(D));
+end;
+
+function TQuaternion.Conjugate: TQuaternion;
+begin
+  result.B := -B;
+  result.C := -C;
+  result.D := -D;
+end;
+
+class operator TQuaternion.Negative(Left: TQuaternion): TQuaternion;
+begin
+  result.A := -Left.A;
+  result.B := -Left.B;
+  result.C := -Left.C;
+  result.D := -Left.D;
+end;
+
+class operator TQuaternion.Positive(Left: TQuaternion): TQuaternion;
+begin
+  result := Left;
+end;
+
+class operator TQuaternion.Add(Left, Right: TQuaternion): TQuaternion;
+begin
+  result.A := Left.A + Right.A;
+  result.B := Left.B + Right.B;
+  result.C := Left.C + Right.C;
+  result.D := Left.D + Right.D;
+end;
+
+class operator TQuaternion.Add(Left: TQuaternion; Right: double): TQuaternion;
+begin
+  result.A := Left.A + Right;
+  result.B := Left.B;
+  result.C := Left.C;
+  result.D := Left.D;
+end;
+
+class operator TQuaternion.Add(Left: double; Right: TQuaternion): TQuaternion;
+begin
+  result.A := Left + Right.A;
+  result.B := Right.B;
+  result.C := Right.C;
+  result.D := Right.D;
+end;
+
+class operator TQuaternion.Subtract(Left, Right: TQuaternion): TQuaternion;
+begin
+  result.A := Left.A - Right.A;
+  result.B := Left.B - Right.B;
+  result.C := Left.C - Right.C;
+  result.D := Left.D - Right.D;
+end;
+
+class operator TQuaternion.Multiply(Left, Right: TQuaternion): TQuaternion;
+begin
+  result.A := Left.A * Right.A - Left.B * Right.B - Left.C * Right.C - Left.D * Right.D;
+  result.B := Left.A * Right.B + Left.B * Right.A + Left.C * Right.D - Left.D * Right.C;
+  result.C := Left.A * Right.C - Left.B * Right.D + Left.C * Right.A + Left.D * Right.B;
+  result.D := Left.A * Right.D + Left.B * Right.C - Left.C * Right.B + Left.D * Right.A;
+end;
+
+class operator TQuaternion.Multiply(Left: double; Right: TQuaternion): TQuaternion;
+begin
+  result.A := Left * Right.A;
+  result.B := Left * Right.B;
+  result.C := Left * Right.C;
+  result.D := Left * Right.D;
+end;
+
+class operator TQuaternion.Multiply(Left: TQuaternion; Right: double): TQuaternion;
+begin
+  result.A := Left.A * Right;
+  result.B := Left.B * Right;
+  result.C := Left.C * Right;
+  result.D := Left.D * Right;
+end;
+
+function TQuaternion.ToString: string;
+begin
+  result := Format('%f + %fi + %fj + %fk', [A, B, C, D]);
+end;
+
+end.

Task/Quaternion-type/Delphi/quaternion-type-2.delphi

@@ -0,0 +1,32 @@
+program QuaternionTest;
+
+{$APPTYPE CONSOLE}
+
+uses
+  Quaternions in 'Quaternions.pas';
+
+var
+  r : double;
+  q, q1, q2 : TQuaternion;
+begin
+  r := 7;
+  q  := q .Init(1, 2, 3, 4);
+  q1 := q1.Init(2, 3, 4, 5);
+  q2 := q2.Init(3, 4, 5, 6);
+
+  writeln('q  = ', q.ToString);
+  writeln('q1 = ', q1.ToString);
+  writeln('q2 = ', q2.ToString);
+  writeln('r  = ', r);
+  writeln('Norm(q ) = ', q.Norm);
+  writeln('Norm(q1) = ', q1.Norm);
+  writeln('Norm(q2) = ', q2.Norm);
+  writeln('-q = ', (-q).ToString);
+  writeln('Conjugate q = ', q.Conjugate.ToString);
+  writeln('q1 + q2 = ', (q1 + q2).ToString);
+  writeln('q2 + q1 = ', (q2 + q1).ToString);
+  writeln('q * r   = ', (q * r).ToString);
+  writeln('r * q   = ', (r * q).ToString);
+  writeln('q1 * q2 = ', (q1 * q2).ToString);
+  writeln('q2 * q1 = ', (q2 * q1).ToString);
+end.