线性变换

transform/RotateSingle.pas

@@ -0,0 +1,79 @@
+program RotateSingle;
+uses
+  Math;
+
+function LinearTrans(arr: array of array of Real; x: array of Real): array of Real;
+var
+  result: array[0..1] of Real;
+  i, j: Integer;
+begin
+  result[0] := x[0]*arr[0][0] + x[1]*arr[0][1];
+  result[1] := x[0]*arr[1][0] + x[1]*arr[1][1];
+  
+  LinearTrans := result;
+end;
+
+function RotateLine(line: array of Real; p: array of Real; dgr: Real): array of Real;
+var
+  k, b: Real;
+  arr: array[0..1, 0..1] of Real;
+  kvec, rkvec: array[0..1] of Real;
+  rk: Real;
+  p1: array[0..1] of Real;
+  pvec, rpvec: array[0..1] of Real;
+  rp1: array[0..1] of Real;
+  result: array[0..1] of Real;
+begin
+  { 
+    Rotate y=kx+b with p for dgr.
+    dgr measured in radians.
+    line: [k, b] => y = kx + b
+  }
+  
+  k := line[0];
+  b := line[1];
+  
+  arr[0][0] := Cos(dgr);
+  arr[0][1] := -Sin(dgr);
+  arr[1][0] := Sin(dgr);
+  arr[1][1] := Cos(dgr);
+  
+  kvec[0] := 1;
+  kvec[1] := k;
+  
+  rkvec := LinearTrans(arr, kvec);
+  rk := rkvec[1] / rkvec[0]; // (a,b) => (1,b/a)
+  
+  p1[0] := 0;
+  p1[1] := b;
+  
+  pvec[0] := p1[0] - p[0];
+  pvec[1] := p1[1] - p[1];
+  
+  rpvec := LinearTrans(arr, pvec);
+  
+  rp1[0] := p[0] + rpvec[0];
+  rp1[1] := p[1] + rpvec[1];
+  
+  result[0] := rk;
+  result[1] := rp1[1] - rk * rp1[0];
+  
+  RotateLine := result;
+end;
+
+var
+  line, p, result: array[0..1] of Real;
+  dgr: Real;
+begin
+  line[0] := 3;
+  line[1] := 4;
+  
+  p[0] := 2;
+  p[1] := 1;
+  
+  dgr := Pi / 4;
+  
+  result := RotateLine(line, p, dgr);
+  
+  WriteLn('Rotated line: k=', result[0]:0:6, ', b=', result[1]:0:6);
+end.