## Polygon table

This is the specification of polygon surface using vertex co-ordinate and other attributes.

1) geometric data table consist of vertex, edges and surface.
2) attribute table consists of degree of transparency and surface reflective etc.
3) some consistency checks of the geometric data table are

•every vertex is listed as an endpoint for at least two ages.
• every edge is the part of at least one polygon.
• every polygon is the closed structure

 Vertex Table V1 V2 V3 V4 V5 x1 y1 z1 x2 y2 z2 x3 y3 z3 x4 y4 z4 x5 y5 z5

 Edge Table E1 E2 E3 E4 E5 V1 V2 V2 V3 V3 V4 V4 V5 V5 V1

 Vertex Table S1 : E1, E2, E6 S2: E3, E4, E5, E6

### Plane equations and visible points

Consider of cube each of 6 planes has two sides inside face and outside face for each plane (in a right-hand coordinates system) if we look its surface and take 3 points in in counter clockwise direction (x1, y1), (x2, y2) and (x3, y3) compute with the four values ABCD as

Then the plane equation at the form
Ax + By + Cz + D = 0
With the following property if
Ax + By + Cz + D < 0
Then x, y point is inside the surface. If
Ax + By + Cz + D > 0 < 1
Then point x, y is outside surface

Read first :- Polygon Mesh Surface

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