# Questions tagged [geometry]

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### Which geometry file format is the most similar to our geometry file format?

To represent a 3D geometry in our software we use this format below: Material-1 Material-2 P1(X1,Y1,Z1) P2(X2,Y2,Z2) P3(X3,Y3,Z3) This 11 point gives us a triangle with the description of what is ...
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### Help understanding tangent from dot product and max distance from component wise vector multiplication

I am looking through this code and seeing two things which confuse me (well, the whole functions does) in the top functions. First, dir * p where ...
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### Methods to interpolate between 2 topologically identical 3D meshes

I have 2 3D surface meshes. These meshes have vertex-correspondence and have the same topology (same edges and triangles connecting the vertices). However, the vertex positions (3d coordinates) are ...
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### What are 'mesh clusters' / hierarchical cluster culling (with LOD?) / triangle cluster culling and how do they relate?

I've seen several references to this and related concepts now but I can't find any hard details about these systems, and how they are implemented. The earliest reference I can find is from the "...
53 views

### Area-light approximation in 2D

I’m trying to render a 2D image something like this: …where an arbitrary shape has its border illuminated by a line in a relatively physically accurate way, i.e. with less illumination reaching the ...
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### Convert point clouds into voxels

I have points that are obtained by sampling a mesh(which is not watertight). Now, I would like to convert that mesh into voxel? Does anyone have any suggestions for solving this problem?
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### Bottom up (as opposed to top down) text on projective geometric algebra?

I have been reading the SIGGRAPH course notes on projective geometric Algebra, and I get some of what's going on. However a lot of the knowledge needed to understand these PGA notes seems to be based ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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,...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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==...
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### Finding geodesics on a mesh?

What are some state of the art methods/algorithms to find geodesics on arbitrary manifold meshes?
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### 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, &...
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### 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 ...
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### 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 ...
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### 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, ...
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### 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 ...
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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
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### 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?