Questions tagged [geometry]
The geometry tag has no usage guidance.
137
questions
0
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1answer
27 views
Computing heat diffusion creates weird results
I am trying to model heat diffusion on the surface of a mesh. I annexed the most important bits of theory about this topic as screenshots on the question see the bottom.
The crux of the issue is we ...
1
vote
1answer
45 views
getting the outline of an arbitrary set of shape unions
I hope this is the right forum to ask this question.
I want to experiment with procedurally generating some buildings, and as a first step I want to generate a 2D shape to use as a foundation for the ...
2
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0answers
38 views
Divide mesh according to level of detail
Background
I need to remesh by OpenVDB, like what Blender remesh does:
Voxel
Uses an OpenVDB to generate a new manifold mesh from the current geometry while trying to preserve the mesh’s original ...
5
votes
1answer
80 views
Existing method to automatically fill in this sort of concavity in meshes?
I am working with a PWP3D-like algorithm that renders silhouettes of a mesh in order to segment a frame of video and update an object's pose. Because it is only the silhouettes of the mesh that matter,...
0
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0answers
38 views
Under what conditions does a mesh operation cause the mesh become non-manifold and how to avoid it?
I'm implementing some mesh operations (e.g. edge collapse, edge split, edge flip etc) and need to ensure applying such operations does not cause the mesh to become non-manifold. However, I'm not sure ...
0
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1answer
39 views
Spline interpolation library in cpp
Have been searching a lot for a good spline interpolation library in cpp, came across one, which is the famous Eigen library , having the unsupported counterpart for spline fitting.<Here>.
I ...
0
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1answer
27 views
Differential or intersection of islands of 2D polygons in different layers
I have a 2D layer/section containing the 2D polygons colored in shades of green.
I have another layer containing the 2D polygons colored in shades of blue.
I intend to figure out how different are ...
0
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1answer
28 views
Render Duplicate Miniature Scene Replica
Context
I am working on project for implementing and user test a World-in-Miniature (WIM) interface for VR. A WIM essentially is a replica of the scene the user is currently in, but in miniature.
...
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0answers
30 views
Changing Coordinate Frames with Affine Transformations
Stuck with this questions could I get some help.
where uA and vA are two orthonormal vectors indicating the two axes, and oA is the origin. Suppose that all three frames of reference shown in ...
0
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1answer
21 views
Moving a vertex through the cursor
There is a way to move a selected point in a mesh with a cursor(assuming a camera that doesn;t change between frames).
The way I remember the algorithm (but seems to be wrong) is:
Unproject the ...
2
votes
0answers
63 views
How to compute a bounding tetrahedron
I'm wondering how to compute a bounding tetrahedron from a set of points so i can initialize a delaunay triangulation
My first approach was to find the bounding box to my set of points and then ...
1
vote
1answer
35 views
Subdivision scheme where the faces and edges have weights (not necessarily scalar weights)
Subdivision schemes work by considering the vertices and their connectivity information to calculate averaging weights.
However, other than specifying which vertices are connected, and perhaps which ...
0
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0answers
45 views
Algorithm to select regions based on curvature on a mesh
I'm trying to understand how to implement an algorithm similar to the one used by Magics' mark surface tool, you can see such behaviour on this video.
Quoting the video: "Basically with this tool ...
0
votes
2answers
64 views
Is there a tool capable of drawing a triangular linear gradient fill?
I need to draw some shapes filled with linear gradients starting from every point and blending smoothly between points, like an OpenGL standard shading (I guess it is called ...
0
votes
1answer
143 views
Vertices, Vertex Normals and Face Normals
Using Open 3D Model Viewer, I have converted an OBJ file to an STL file.
In the source file, the Vertex Normals are specified and in the destination, the face normal of the triangles are present which ...
0
votes
2answers
88 views
Rounding a 3D corner with Subdivisions
Following the instructions from this post on Stack Overflow, I have been able to find points A, B, and C from points V1, V2, and V3 and a radius value (code below). I would like to be able to find a ...
0
votes
1answer
35 views
In place sorting of a half edge DS?
Cross posting from SO because I didn;t know where to put this question.
I have an implementation of the half edge and I am trying to sort the edges such that edge n+1 is the pair of edge n.
Setup
I ...
3
votes
1answer
58 views
Why is the valence of regular vertices 6?
So I recently learnt that supposedly for any mesh, and pretty much any scheme, the valence of regular vertices must be 6. It seems to be related to the Euler-Poincare formula but I have not been able ...
2
votes
1answer
53 views
Sort half-edges around common vertex in 3d [closed]
I'm trying to figure out this problem for very long time and am no getting nowhere. I'm working on a simple 3d modeler that uses half-edge data structure.
Say I have non-manifold geometry where two ...
1
vote
1answer
55 views
Improve accuracy of mesh gradient?
So to make it simple. I currently use a method I found online to compute the gradient of a scalar field of a mesh.
To test how accurate this is, I made a sphere and followed the gradient direction of ...
3
votes
1answer
47 views
Mis understanding of the Heat Method
I have been trying to understand a paper in CG for a while, called the Heat Method by Ken
Many things have clicked but I don't fully understand it yet. In particular.
In the following $u$ is a vector ...
4
votes
1answer
57 views
Gradient descent (Not ML) on arbitrary meshes
So I am doing a gradient descent like algorithm on the surface of a mesh and I just noticed something:
The above is the geodesic gradient (the distance to a single vertex)
Look at where the ear ...
2
votes
2answers
114 views
Smart half edge iteration?
In my HE implementation, half edges are stored in an array. When I iterate over the edges, I color all the HE black, and when I do an operation on an edge (e.g edge splitting) I mark both the current ...
1
vote
2answers
84 views
Discrete Gradient?
I am trying to understand how to get the discrete gradient of a mesh that is being used as the input of some function $f$. In other words for every vertex $v$ there is a scalar quantity $s$ associated ...
1
vote
2answers
70 views
Heat Method (Crane et Al) How do we pick u?
The heat method is a very interesting paper for distance computation:
https://www.cs.cmu.edu/~kmcrane/Projects/HeatMethod/paperCACM.pdf
The idea behind the paper is that, heat travels along the ...
0
votes
1answer
34 views
Is the laplacian operator for meshes just the sum of the differences of neighbouring vertices?
I am starting to learn about the laplacian operator $\Delta = \nabla \cdot \nabla\phi(p)$
Which can be described as the divergence of the gradient of a scalar function $\phi$. This is equivalent to ...
0
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0answers
8 views
MMP algorithm, no metion of “in window” intersections
If you are familiar with the MMP algorithm for geodesic finding, you know an important part of the algorithm revolves around solving intersections of windows.
I am running into a case that I don't see ...
1
vote
1answer
75 views
Approximating Geodesics in a half edge DS, how can I refine my mesh to get good approximations
I implemented Djikstra's shortest path algorithm to approximate Geodesics on arbitrary meshes. Djikstra's works, but I noticed a problem inherent to the discretization of my meshes.
Consider the ...
1
vote
0answers
54 views
The ploygon width parallel to the x axis as a function of the y ordonate?
Considering a polygon with n vertices as input.
I need to calculate the integral of the form
\[\int_A p(y) dA \] where $p(y)$ is a piecewise polynomial function of $y$.
May be if I could find the ...
0
votes
1answer
42 views
Fast and exact Geodesics on meshes, Backtracking confusion
The following is an excerpt from a 2005 paper on geodesics on triangular meshes, taken from section 3.5
In this case $p$ is a point on some arbitrary face in a mesh, $p'$ is a point on one of the 3 ...
0
votes
0answers
27 views
MMP Geodesic algorithm I need clarification
I am reading the 1987 paper on Geodesics on polyhedra and I am confused on something.
The paper states:
If $I1==NIL$, the channel is simply that part of $f’$ to the left of $\beta_2c_2$; and if
$I2==...
1
vote
1answer
52 views
Finding geodesics on a mesh?
What are some state of the art methods/algorithms to find geodesics on arbitrary manifold meshes?
3
votes
1answer
95 views
Are some 3D objects “solid”? Do they have internal density? If so, when, and in which file formats?
I am more or less a complete novice in the field of 3D modeling. I understand the basics of a polygon mesh and a texture; however, it was always my understanding that 3D models were, effectively, &...
3
votes
2answers
182 views
Why are texture coordinates often called UVs?
Is there some historical reason texture coordinates are often called UVs? I get that vertex positions are x, y, z but even OpenGL has TEXTURE_WRAP_S and ...
5
votes
1answer
676 views
How does UV unwrapping work?
I would like to project the triangles of my mesh to a 2D surface. I would like to minimalize the distorion, avoid breaking connected polygons if possible, and also maximalize the used space on the 2D ...
0
votes
0answers
51 views
How does on the fly LOD work?
In the Unreal Engine 5 tech demo, they mention, that there is no need to manually generate LOD levels for each model, because the on the fly LOD system will generate polygons from the original mesh, ...
1
vote
1answer
81 views
Has anyone found an analytic solution to the product of spherical gaussians from Xu et al?
In section 4.2 of this paper:
http://cseweb.ucsd.edu/~ravir/274/15/papers/a209-xu.pdf
Xu et al approximate the product of 2 anisotropic Gaussian distributions. I want to know if someone has found not ...
1
vote
0answers
67 views
Why does processing dense geometry consume less power than simple geometry?
In The Road to PS5, Mark Cerny states:
It's counter-intuitive, but processing dense geometry typically consumes less power than processing simple geometry.
Why is this the case?
0
votes
0answers
63 views
Consistent Video Depth Estimation from Monocular Lens to approximate LiDAR?
If the iPhone had LiDAR sensors, it would be possible to generate a 3D point cloud that you could theoretically use to furnish a 3D AR reconstruction of your surroundings. E.g. you could create an AR ...
2
votes
1answer
70 views
Off by one error when creating face indices
I seem to have an off by one error when creating the indices for the faces of a sphere and I can't understand where.
The exact problem is that when I try to calculate the normals of each face a dark ...
1
vote
2answers
307 views
Calculate normals from vertices
Assume you have a list of vertices and their connectivity information. (I.e you can find all the adjacent edges and faces to each vertex).
What is a good approach to calculate a normal from this ...
0
votes
1answer
60 views
How do you compute the winding number of a closed poly curve?
Pretty much the title, given a closed curve in 2D, defined by a set of points, and a point. What's the algorithm to calculate the winding number of that curve, point pair?
0
votes
2answers
287 views
Looking for a cylinder / axis-aligned box volume intersection test
Given:
An arbitrary circular cylinder (defined by startpoint, endpoint, and radius). An Infinite cylinder is acceptable as well, as long as it passes through those points and has the same radius.
An ...
0
votes
1answer
50 views
Determining shortest vector between a ray and an axis-aligned 3D bounding box (correcting a near-miss)
I have a situation where (due to floating point error) a ray that is known to hit a bounding box fails due to floating point error. (1e-8 or so)
Expanding the box is not an acceptable solution in my ...
1
vote
1answer
165 views
How to handle Half edge boundary edge iteration from vertex?
Ok so let's say we have a portion of a mesh that looks somewhat like this:
A triangle fan with one of the triangles removed. If that triangles was not removed, we could get all the edges adjacent to ...
2
votes
1answer
69 views
How to subdivide faces with a half edge DS?
Assume we have a mesh represented as a half edge datastructure.
We want to subdivide faces without introducing unnecessary vertices (i.e the new number of vertices must be exactly V + E where V is the ...
0
votes
1answer
169 views
Reading thesis on cone tracing, did the author make a mistake?
I am reading this document that talks about signed distance field rendering.
In that document section 6.3, on the topic of cone tracing, it says:
Cone tracing is an extension of the sphere tracing ...
1
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0answers
70 views
What other geometry processing data structures are there?
I essentially know of 2 geometry processing data structures. one is the half edge (which has some really nice properties, but can't represent non manifold meshes nor tet meshes).
The other is an ...
4
votes
3answers
152 views
Visualize the interpolated unit quaternion on the surface of the unit sphere
My major is mechanical, please forgive me for asking questions that may seem trivial to you.
First, I'm reading the following paper:
Dam, Erik B., Martin Koch, and Martin Lillholm. Quaternions, ...
1
vote
0answers
28 views
Boundary Smoothing Algorithms
I have a 2-manifold with boundary, built with marching cubes. Are there any well-known algorithms for smoothing its boundary edges?
Most of the papers I found are concerned with smoothing the surface....
