From c111a2090c180f124e824ce9cac2bf6ed387a0e7 Mon Sep 17 00:00:00 2001
From: Nico de Poel <ndepoel@gmail.com>
Date: Thu, 9 Feb 2023 10:56:39 +0100
Subject: [PATCH] Implemented a more accurate face area computation, allowing
 for more precise tessellation LOD selection. Also started putting
 face-related functions into a separate source file.

---
 PS1BSP.vcxproj         |  2 ++
 PS1BSP.vcxproj.filters |  6 +++++
 face.cpp               | 54 ++++++++++++++++++++++++++++++++++++++++++
 face.h                 |  3 +++
 main.cpp               | 34 ++++----------------------
 5 files changed, 69 insertions(+), 30 deletions(-)
 create mode 100644 face.cpp
 create mode 100644 face.h

diff --git a/PS1BSP.vcxproj b/PS1BSP.vcxproj
index bb52a8d..848b7a8 100644
--- a/PS1BSP.vcxproj
+++ b/PS1BSP.vcxproj
@@ -142,6 +142,7 @@
     </Link>
   </ItemDefinitionGroup>
   <ItemGroup>
+    <ClCompile Include="face.cpp" />
     <ClCompile Include="gpc.cpp" />
     <ClCompile Include="lighting.cpp" />
     <ClCompile Include="main.cpp" />
@@ -152,6 +153,7 @@
   <ItemGroup>
     <ClInclude Include="bsp.h" />
     <ClInclude Include="common.h" />
+    <ClInclude Include="face.h" />
     <ClInclude Include="gpc.h" />
     <ClInclude Include="lighting.h" />
     <ClInclude Include="matrix.h" />
diff --git a/PS1BSP.vcxproj.filters b/PS1BSP.vcxproj.filters
index eb8a372..e7b3a06 100644
--- a/PS1BSP.vcxproj.filters
+++ b/PS1BSP.vcxproj.filters
@@ -36,6 +36,9 @@
     <ClCompile Include="tesselate.cpp">
       <Filter>Source Files</Filter>
     </ClCompile>
+    <ClCompile Include="face.cpp">
+      <Filter>Source Files</Filter>
+    </ClCompile>
   </ItemGroup>
   <ItemGroup>
     <ClInclude Include="bsp.h">
@@ -86,6 +89,9 @@
     <ClInclude Include="matrix.h">
       <Filter>Header Files</Filter>
     </ClInclude>
+    <ClInclude Include="face.h">
+      <Filter>Header Files</Filter>
+    </ClInclude>
   </ItemGroup>
   <ItemGroup>
     <CopyFileToFolders Include="palette.lmp">
diff --git a/face.cpp b/face.cpp
new file mode 100644
index 0000000..675c882
--- /dev/null
+++ b/face.cpp
@@ -0,0 +1,54 @@
+#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;
+}
diff --git a/face.h b/face.h
new file mode 100644
index 0000000..4308d91
--- /dev/null
+++ b/face.h
@@ -0,0 +1,3 @@
+#pragma once
+
+double face_computeArea(const world_t* world, const face_t* face);
diff --git a/main.cpp b/main.cpp
index c3c4452..062bc13 100644
--- a/main.cpp
+++ b/main.cpp
@@ -4,6 +4,7 @@
 #include "ps1bsp.h"
 #include "lighting.h"
 #include "texture.h"
+#include "face.h"
 #include "tesselate.h"
 
 static char path[_MAX_PATH];
@@ -43,35 +44,6 @@ size_t writeAtlasData(const char* timPath, ps1bsp_dentry_t& dentry, FILE* f)
 	return written;
 }
 
-static float computeFaceArea(const world_t* world, const face_t* face)
-{
-	const plane_t* plane = &world->planes[face->plane_id];
-
-	// Construct a tangent and bitangent for the plane
-	Vec3 tangent, bitangent;
-	plane->getTangents(tangent, bitangent);
-
-	// Project all face vertices onto the face's plane
-	BoundBox bounds;
-	for (int edgeListIdx = 0; edgeListIdx < face->ledge_num; ++edgeListIdx)
-	{
-		int edgeIdx = world->edgeList[face->ledge_id + edgeListIdx];
-		int vertIndex = edgeIdx > 0 ?
-			world->edges[edgeIdx].vertex0 :
-			world->edges[-edgeIdx].vertex1;
-
-		const vertex_t* vertex = &world->vertices[vertIndex];
-		Vec3 vec = vertex->toVec();
-
-		double x = tangent.dotProduct(vec);
-		double y = bitangent.dotProduct(vec);
-		bounds.includePoint(Vec3(x, y, 0.0));
-	}
-
-	Vec3 extents = bounds.max - bounds.min;
-	return extents.x * extents.y;
-}
-
 typedef std::unordered_map<const face_t*, std::vector<Tesselator::Polygon>> FacePolygons;
 
 int process_faces(const world_t* world, const TextureList& textures)
@@ -156,7 +128,7 @@ int process_faces(const world_t* world, const TextureList& textures)
 
 		outFace.numFaceVertices = (unsigned char)(outFaceVertices.size() - outFace.firstFaceVertex);
 		outFace.center = (vertexSum / face->ledge_num).convertWorldPosition();
-		float area = computeFaceArea(world, face);
+		double area = face_computeArea(world, face);
 		outFace.center.pad = (short)(area / 100);
 		outFaces.push_back(outFace);
 	}
@@ -290,6 +262,8 @@ int process_faces(const world_t* world, const TextureList& textures)
 
 		outFace->numPolygons = (unsigned char)(outPolygons.size() - outFace->firstPolygon);
 		outFace->center.pad = (short)sqrt((double)outFace->center.pad * 100 / outFace->numPolygons);
+		if (outFace->center.pad <= 0)
+			outFace->center.pad = 1;	// Prevent division by zero in the LOD calculation
 	}
 
 	printf("Converting data...\n");