#include "common.h"
#include "bsp.h"
#include "face.h"

// Heron's formula, yoinked from: https://www.cuemath.com/measurement/area-of-triangle/
static double face_triangleArea(Vec3 v0, Vec3 v1, Vec3 v2)
{
	double a = (v1 - v0).magnitude();
	double b = (v2 - v0).magnitude();
	double c = (v0 - v2).magnitude();
	double s = (a + b + c) * 0.5;

	double areaSqr = s * (s - a) * (s - b) * (s - c);
	if (areaSqr < FLT_EPSILON)	// Collapsed triangles can happen, prevent NaN in that situation
		return 0.0;

	return sqrt(areaSqr);
}

double face_computeArea(const world_t* world, const face_t* face)
{
	int i0, i1, i2;

	// Get the first edge so we can build a triangle fan
	int edgeIdx = world->edgeList[face->ledge_id];
	if (edgeIdx > 0)
	{
		i0 = world->edges[edgeIdx].vertex0;
		i1 = world->edges[edgeIdx].vertex1;
	}
	else
	{
		i0 = world->edges[-edgeIdx].vertex1;
		i1 = world->edges[-edgeIdx].vertex0;
	}

	// Triangulate the face, compute the area of each triangle and add them all together
	double totalArea = 0.0;
	for (int edgeListIdx = 1; edgeListIdx < face->ledge_num - 1; ++edgeListIdx)
	{
		int edgeIdx = world->edgeList[face->ledge_id + edgeListIdx];
		i2 = edgeIdx > 0 ? world->edges[edgeIdx].vertex0 : world->edges[-edgeIdx].vertex1;

		Vec3 v0 = world->vertices[i0].toVec();
		Vec3 v1 = world->vertices[i1].toVec();
		Vec3 v2 = world->vertices[i2].toVec();

		totalArea += face_triangleArea(v0, v1, v2);

		i1 = i2;
	}

	return totalArea;
}