c - 如何用开罗创建同心三角形？

Question

我有三个点形成一个三角形（显然）。但我不想画这个三角形，而是画一个较小的三角形。

我如何在 C 中使用 Cairo 来做到这一点？

Answer 1

我认为您需要计算边与旧三角形边等距的新三角形的顶点。

求相邻三角形边BD = BA / |BA|, BE = BC / |BC|的单位向量 ... (|BA| 是向量 BA 的长度)

求单位平分线BF = (BD + BE) / |BD + BE|

找到 F 点的最终位置（所需长度的平分线）BF = BF * NeededDistance / ( BF x BE ) ...（分母是叉积，它等于 Sin(ABC/2)

对 G 和 H 顶点执行相同的操作。

Delphi 代码和结果：

var
  P, V: array[0..2] of TPoint;
  i, inext, iprev: Integer;
  nx, ny, px, py, mx, my, coeff: Double;
  distance: Integer;

  procedure NormalizeVector(var dx, dy: Double);
  var
    revlen: Double;
  begin
    revlen := 1.0 / Hypot(dx, dy);
    dx := dx * revlen;
    dy := dy * revlen;
  end;

begin
  Canvas.Brush.Color := Color;
  Canvas.FillRect(ClientRect);  //clean the blackboard
  Randomize;

  //big triangle vertices
  for i := 0 to 2 do
    P[i] := Point(Random(500), Random(500));

  //draw big triangle
  Canvas.Brush.Style := bsClear;
  Canvas.Polygon(P);

  for i := 0 to 2 do begin
    inext := (i + 1) mod 3;  // next vertice index
    iprev := (i - 1 + 3) mod 3;  // previous vertice index
    nx := P[inext].X - P[i].X;   //vector to the next vertice
    ny := P[inext].Y - P[i].Y;
    px := P[iprev].X - P[i].X;   //vector to the previous vertice
    py := P[iprev].Y - P[i].Y;

    NormalizeVector(nx, ny);  //make unit vectors
    NormalizeVector(px, py);

    mx := nx + px;
    my := ny + py;
    NormalizeVector(mx, my); //unit bisector

    distance := 20;
    coeff := distance / (mx * py - my * px);
    mx := mx * coeff;
    my := my * coeff;

    //inner triangle vertice
    V[i] := Point(P[i].X + Round(mx), P[i].Y + Round(my));
  end;

  //draw inner triangle
  Canvas.Polygon(V);