layout: default title: "Bevelling" permalink: /meshedit/local/bevel/ parent: "Local Operations" grand_parent: "A2: MeshEdit" usemathjax: true
Here we provide some additional detail about the bevel operations and their implementation in Scotty3D. Each bevel operation has two components:
The methods that update the connectivity are
The methods that update geometry are
HalfedgeMesh::extrude_vertex will update both connectivity and geometry, as it should first perform a flat bevel on the vertex, and then insert a vertex into the new face.
The methods for updating connectivity can be implemented following the general strategy outlined in edge flip tutorial. Note that the methods that update geometry will be called repeatedly for the same bevel, in order to adjust positions according to user mouse input. See the gif in the User Guide for a demonstration on how the mouse's movement affects the positioning.
To update the geometry of a beveled element, you are provided with the following data:
start_positions- These are the original vertex positions of the beveled mesh element, without any insetting or offsetting.
face- This is a reference to the face currently being beveled. This was returned by one of the connectivity functions.
tangent_offset- The amount by which the new face should be inset (i.e., "shrunk" or "expanded")
normal_offset- (faces only) The amount by which the new face should be offset in the normal direction.
Also note that we provide code to gather the halfedges contained in the beveled face, creating the array
new_halfedges. You should only have to update the position (
Vertex::pos) of the vertices associated with this list of halfedges. The basic recipe for updating these positions is:
start_positions, or the members
Vertex::posfor the vertices of the new, beveled polygon only (i.e., the vertices associated with each of
The reason for storing
start_positions in an array is that it makes it easy to access positions "to the left" and "to the right" of a given vertex. For instance, suppose we want to figure out the offset from the corner of a polygon. We might want to compute some geometric quantity involving the three vertex positions
start_positions[i+1] (as well as
inset), then set the new vertex position
new_halfedges[i]->vertex()->pos to this new value:
A useful trick here is modular arithmetic: since we really have a "loop" of vertices, we want to make sure that indexing the next element (+1) and the previous element (-1) properly "wraps around." This can be achieved via code like
// Get the number of vertices in the new polygon int N = (int)hs.size(); // Assuming we're looking at vertex i, compute the indices // of the next and previous elements in the list using // modular arithmetic---note that to get the previous index, // we can't just subtract 1 because the mod operation in C++ // doesn't behave quite how you might expect for negative // values! int a = (i+N-1) % N; int b = i; int c = (i+1) % N; // Get the actual 3D vertex coordinates at these vertices Vec3 pa = start_positions[a]; Vec3 pb = start_positions[b]; Vec3 pc = start_positions[c];
From here, you will need to compute new coordinates for vertex
i, which can be accessed from
new_halfedges[i]->vertex()->pos. As a "dummy" example (i.e., this is NOT what you should actually do!!) this code will set the position of the new vertex to the average of the vertices above:
new_halfedges[i]->vertex()->pos = ( pa + pb + pc ) / 3.; // replace with something that actually makes sense!
The only question remaining is: where should you put the beveled vertex? We will leave this decision up to you. This question is one where you will have to think a little bit about what a good design would be. Questions to ask yourself:
Face::normal()here or think of another way to compute the face's normal. (What directions would make sense for a vertex to be shifted when we move our mouse up and down?)
The best way to get a feel for whether you have a good design is to try it out! Can you successfully and easily use this tool to edit your mesh? Or is it a total pain, producing bizarre results? You be the judge!
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