How to create concentric triangles with Cairo? - c

Question

I have three points that form a triangle (obviously). But I don't want to draw this triangle but a smaller one inside.
How do I do that with Cairo in C?

Answer 1

I think you need to calculate the vertices of new triangle whose sides are equidistant from the sides of the old triangle.
Find unit vectors for adjacent triangle sides BD = BA / |BA|, BE = BC / |BC| ... (|BA| is length of vector BA)
Find unit bisector BF = (BD + BE) / |BD + BE|
Find final position of F point (bisector of needed length) BF = BF * NeededDistance / (BF x BE) ...(denominator is cross product, it is equal to Sin(ABC/2)
Do the same for G and H vertices.
Delphi code and result:
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);