Ordering Line Segments to form a 2D Polygon after slicing a 3D Tri Map

In summary, The speaker describes a method for slicing a 3D shape and computing the intersections of the plane and triangle faces to obtain line segments for a 2D polygon. The problems faced include unordered line segments, rounding errors, and disjointed polygons. The speaker suggests considering slicing segments instead of triangles to potentially simplify the process.
  • #1
nucloxylon
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0
I have a 3D shape described by a triangulation map i.e. a map between the vertices to the faces of the shape which are all triangles.

I then sliced the shape by a plane and computed the intersections of the plane and the triangle faces. Each triangle face that intersects the plane, will have two intersection points on two of it's edges thus giving me a line segment that would be apart of the 2D polygon I'm hoping to get out of slicing.

There are a few problems though. For one thing the Line Segments are not ordered. Also, because of some rounding errors, two adjacent line segments might not share the EXACT same point so there has to be some kind of tolerance. Finally the biggest problem I'm facing is that the polygon might be disjointed i.e. the 3D object is not convex, so the polygon slice might be made up of several different polygons.

From a programming perspective, anyone know a fast method to do this and how to deal with the multiple polygons?
 
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  • #2
Maybe instead of thinking about slicing triangles to get segments (whose endpoints you then have to match up, worrying about rounding errors and such), you could think about slicing segments to get points. You know which segments belong to the same triangle, and therefore which pairs of resulting points need to have an edge between them, as well as an ordering for each pair (i.e. a normal vector). That might be all you need.
 

What is the purpose of ordering line segments to form a 2D polygon?

The purpose of ordering line segments to form a 2D polygon is to create a complete and accurate representation of the original 3D Tri Map. By arranging the line segments in a specific order, we can create a 2D polygon that accurately reflects the shape and dimensions of the 3D object.

What is the process for ordering line segments to form a 2D polygon?

The process for ordering line segments to form a 2D polygon involves slicing the 3D Tri Map into 2D cross-sections, identifying and labeling the line segments within each cross-section, and then arranging the line segments in a specific order to create a complete polygon.

Why is it important to accurately order the line segments?

Accurately ordering the line segments is important because it ensures that the 2D polygon accurately represents the shape and dimensions of the original 3D Tri Map. If the line segments are not ordered correctly, the resulting polygon may be distorted or incomplete.

What factors can affect the order of the line segments?

The order of the line segments can be affected by various factors such as the orientation of the 3D object, the direction of the slicing plane, and the complexity of the object's shape. It is important to carefully consider these factors when ordering the line segments to ensure an accurate representation.

Are there any tools or techniques that can aid in ordering line segments for a 2D polygon?

Yes, there are several tools and techniques that can aid in ordering line segments for a 2D polygon. These include computer software programs, geometric algorithms, and manual methods such as using rulers and protractors to measure and arrange the line segments.

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