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First, to preface: the reason it's hard to find details about these hierarchical cluster culling systems because they are a still emerging field, at the very cutting edge of real-time rendering development. Only a handful of games/engines have successfully shipped something like this, and mostly not open source (UE5 being a recent exception). It is an area ...

3

What you are looking for is semi-sharp creases. You can find it in section 3 of this paper: https://graphics.pixar.com/library/Geri/paper.pdf Basically, each edge is given a sharpness value $s$. This can either be a integer or a floating point value. This value signifies how many subdivision steps this edge will be subdivided using sharp-subdivision rules. ...

3

After a fair bit of reading and skimming through papers, I have yet to find a good definition other than "indent" for what I want to remove, but I have found answers to pretty much everything else. The concept of a "Visual Hull" is what I was looking for regarding a mesh that doesn't have these indents. While the Wikipedia page, and a ...

3

Found a solution—it may not be strictly accurate for 2D, but it produces the look that I’m after. “Linear Light Shading with Linearly Transformed Cosines”, in section 1.3, describes a closed-form solution to this integral; transforming the line’s endpoints into a space local to the surface and then running them through the I_diffuse_line function from ...

2

There is very little geometrical meaning to the multiplication of two vectors and there are no well defined identities describing the result. But that doesn't make it illegal, and is an important part of many well defined functions such as the dot product. Multiplication of vectors also have several important identities that allow terms to be moved around in ...

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Draw it twice, first time at full size and the color you want for the outline, draw it filled. The second time you draw it scaled down in both the x and y directions. The second time you draw it the color is the same as the background color, and draw it filled again. What will be left is the outline. Is this what you had in mind? Per your comment, I add more ...

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So you have a series of points and, at each point, a supplied derivative? Is a piecewise cubic sufficient or does it need higher derivative continuity? If the former is ok, then Cubic Hermite Splines will do the job. (If you need, they can be trivially mapped into cubic Beziers)

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In CGAL, there is the Arrangement package that allows to build a topologically valid planar partition given a set of segments, and the Regularized Boolean Set-Operations that provides boolean operations between polygons.

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Most 2D graphics programs are able to do linear gradients with arbitrary orientations. If you don't mind a little work, it is possible to set this up to imitate the 2D linear interpolation across a triangle. Set up two layers: Pick two of the colors, say red and green, and set up a linear gradient between those two colors along the red-green edge. In a ...

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I'm not familiar with the exact nuances of the STL format, but here are some answers on general computer graphics principles: In the source file, the Vertex Normals are specified and in the destination, the face normal of the triangles are present which are different than the normals one would get by (a-b) x (a-c), where a, b, c are the vertex coordinates ...

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