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Polygon meshes for 3D objects

Short answer

Polygon meshes represent a 3D object as a collection of vertices, edges, and polygonal faces that approximate its surface. Vertices are shared, transformations apply only to vertices, and triangles are always planar, making rendering simple and efficient.

How do polygon meshes support representing a 3D object? Explain with relevant figures.

A polygon mesh is a collection of vertices, edges and faces (polygons) that share vertices and edges and together approximate the surface of a 3D object. Because graphics hardware works with polygons, the mesh is the most common way to represent 3D objects.

Common forms:

  • Triangle strip: a series of connected triangles where each new vertex adds one triangle. n vertices give n − 2 triangles.
  • Quadrilateral mesh: an n × m array of vertices gives (n − 1)(m − 1) quadrilaterals.
  • Triangle fan: triangles sharing one common vertex.
Triangle strip:         Quad mesh:
 V1--V3--V5--V7        +--+--+--+
  \ / \ / \ /          |  |  |  |
   V2--V4--V6          +--+--+--+
                       |  |  |  |
                       +--+--+--+

How the mesh supports 3D objects:

  1. Planar and curved surfaces are approximated; finer meshes give a smoother surface.
  2. Vertices are shared, saving storage and keeping the surface connected.
  3. Transformations are applied to vertices only.
  4. Face normals and vertex normals support shading, and each polygon can be filled with colour or texture.
  5. Triangles are always planar, which makes rendering simple.

The mesh is stored in vertex, edge and surface tables.

✓ Answer checked by Claude Opus 5.5 (high effort)

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