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Determining and Fixing Warped 3D Polygon Faces

Identifying Warped Faces

A polygon face in 3D space is considered warped (or non-planar) when its vertices don’t all lie on the same plane. Here are methods to determine if a face is warped:

1. Normal Vector Method:

   • Calculate the normal vector for each possible triangle within the polygon
   • If the normals differ significantly, the face is warped

2. Plane Equation Method:

   • Calculate the plane equation from three non-collinear vertices
   • Check if all other vertices satisfy this plane equation within a tolerance (e.g., distance < 0.001 units)

3. Area Comparison Method:

   • Calculate the 3D area of the polygon
   • Project it onto its best-fit plane and calculate the 2D area
   • If the difference exceeds your threshold, it’s warped

Splitting Warped Faces into Planar Faces

1. Triangulation Approach

The simplest method is to triangulate the face:

• Split the polygon into triangles using ear-clipping or other triangulation methods
• Each triangle is guaranteed to be planar

2. Newell’s Algorithm for Best-Fit Plane

1. Calculate the best-fit plane using Newell’s method
2. Project all vertices onto this plane
3. Use the 2D projected coordinates to find natural splitting lines

3. Edge Split Method

1. Identify the vertex farthest from the best-fit plane
2. Split the polygon along edges that connect to this vertex
3. Recursively check and split the new faces until all are planar

4. Convex Decomposition

For complex warped polygons:

1. Compute the convex hull of the vertices
2. Split along the hull edges that aren’t part of the original polygon
3. Repeat for any remaining non-planar faces

Implementation Example (Pseudocode)

function isPlanar(vertices, tolerance):if vertices.count <= 3: return trueplane = calculateBestFitPlane(vertices)for vertex in vertices:if distance(vertex, plane) > tolerance:return falsereturn truefunction splitWarpedFace(face, maxDeviation):if isPlanar(face.vertices, maxDeviation):return [face]// Find the vertex farthest from the planeplane = calculateBestFitPlane(face.vertices)farthestVertex = findFarthestVertex(face.vertices, plane)// Split along edges connected to farthest vertexconnectedEdges = getConnectedEdges(farthestVertex)newFaces = []for edge in connectedEdges:newFace = createNewFace(edge, face.vertices)newFaces += splitWarpedFace(newFace, maxDeviation)return newFaces

Considerations

• Choose an appropriate tolerance value based on your application
• For rendering purposes, triangulation is often sufficient
• For CAD/CAM applications, more precise splitting methods may be needed
• Preserve texture coordinates and vertex attributes when splitting

资料

Warped-Face Gradient Correction
36.21. Convergence and Stability
【Fluent案例】20：MRF模型