Background and motivation
The Perp Dot Product can be used to check the winding order of triangle vertices, check if a point is inside a triangle, calculate barycentric coordinates of a point inside a triangle, triangulate polygons by ear clipping method, etc.
API Proposal
namespace System.Numerics;
public struct Vector2
{
public static float PerpDot(Vector2 value1, Vector2 value2)
{
return value1.X * value2.Y - value1.Y * value2.X;
}
}Alternative design:
namespace System.Numerics;
public struct Vector2
{
public static float PerpDot(Vector2 value1, Vector2 value2)
{
return Dot(new Vector2(-value1.Y, value1.X), value2);
}
}API Usage
using System.Numerics;
public bool ClockwiseTriangle(Vector2 a, Vector2 b, Vector2 c)
{
return Vector2.PerpDot(b - a, c - a) < 0;
}
public bool PointInTriangle(Vector2 p, Vector2 a, Vector2 b, Vector2 c)
{
float u = Vector2.PerpDot(b - p, c - p);
float v = Vector2.PerpDot(c - p, a - p);
float w = Vector2.PerpDot(a - p, b - p);
return (u >= 0 && v >= 0 && w >= 0) ||
(u <= 0 && v <= 0 && w <= 0);
}
public (float, float, float) Barycentric(Vector2 p, Vector2 a, Vector2 b, Vector2 c)
{
float denom = 1f / PerpDot(b - a, c - a);
float u = Vector2.PerpDot(b - p, c - p) * denom;
float v = Vector2.PerpDot(c - p, a - p) * denom;
return (u, v, 1 - u - v);
}Alternative Designs
No response
Risks
No response
Background and motivation
The Perp Dot Product can be used to check the winding order of triangle vertices, check if a point is inside a triangle, calculate barycentric coordinates of a point inside a triangle, triangulate polygons by ear clipping method, etc.
API Proposal
Alternative design:
API Usage
Alternative Designs
No response
Risks
No response