Metal shader determine point inside a convex quadrilateral - ios

Question

Is there a builtin way in Metal shading language to determine if a point lies inside a convex quadrilateral (or convex polygon in general)? If not, what is the quickest way to determine the same?

Answer 1

I have not been able to find a metal function that meets your needs. I will propose what I believe to be a relatively fast solution (although please feel free to critique or improve it). Note that I have assumed you are working in 2D (or at least a 2D frame for a polygon whose vertices are coplanar)
constant constexpr float M_PI = 3.14159265358979323846264338327950288;
constant constexpr float2 iHat = float2(1, 0);
namespace metal {
// The sawtooth function
METAL_FUNC float sawtooth(float f) { return f - floor(f); }
/// A polygon with `s` sides oriented with `transform` that converts points from the system within which the polygon resides.
/// The frame "attached" to the polygon has an X axis passing through a vertex of the polygon. `circR` refers to the radius
/// of the circumscribed circle that passes through each of the verticies
struct polygon {
const uint s;
const float circR;
const float3x3 transform;
// Constructor
polygon(uint s, float circR, float3x3 transform) : s(s), circR(circR), transform(transform) {}
// `pt` is assumed to be a point in the parent system. `conatins` excludes the set of points along the edges of the polygon
bool contains(float2 pt);
};
}
bool metal::polygon::contains(float2 pt) {
// The position in the frame of the polygon
float2 poly_pt = (transform * float3(pt, 1)).xy;
// Using the law of sines, we can determine the distance that is allowed (see below)
float sqDist = distance_squared(0, poly_pt);
// Outside circle that circumscibes the polygon
if (sqDist > circR * circR) return false;
// Calculate the angle the point makes with the x axis in the frame of the polygon.
// The wedgeAngle is the angle that is formed between two verticies connected by an edge
float wedgeAngle = 2 * M_PI / s;
float ptAngle = dot(poly_pt, iHat);
float deltaTheta = sawtooth(ptAngle / wedgeAngle) * wedgeAngle;
// Calculate the maximum distance squared at this angle that is allowed at this angle relative to
// line-segment joining the `floor(ptAngle / wedgeAngle)`th (kth) vertex with the center of the polygon.
// This is done by viewing the polygon from a frame whose X-axis is the line from the center of the polygon
/// to the kth vertex. Draw line segment L1 from the kth vertex to the (k+1)th vertex and mark its endpoints K and L respectively.
/// Draw line segment L2 from the center of the polygon to the point under consideration and mark L2's intersection with L1
/// as "A". If the center of the triangle is "O", then triangle "OKL" is isosceles with vertex angle `wedgeAngle` and
/// base angle B = M_PI / 2 - wedgeAngle / 2 (since 2B + wedge = M_PI). Triangle "OAK" contains `deltaTheta` and B.
/// Thus, the third angle is M_PI - B - deltaTheta. `maxR` results from the law of sines with this third angle and the
/// base angle B' contained within triangle "OAK".
float maxR = circR * sin(M_PI / 2 - wedgeAngle / 2) / sin(M_PI / 2 + wedgeAngle / 2 - deltaTheta);
return sqDist < maxR * maxR;
}
Note that I opted for a constexpr value in lieu of a macro declaration. Either would do.