# Questions tagged [geometry]

The tag has no usage guidance.

126 questions
Filter by
Sorted by
Tagged with
35 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 ...
17 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 ...
71 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 ...
20 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 ...
48 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 ...
34 views

### Sort half-edges around common vertex in 3d

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 ...
31 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 ...
37 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 ...
48 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 ...
110 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 ...
61 views

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 ...
67 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 ...
30 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 ...
7 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 ...
73 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 ...
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 ...
38 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 ...
25 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==...
48 views

### Finding geodesics on a mesh?

What are some state of the art methods/algorithms to find geodesics on arbitrary manifold meshes?
78 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, &...
166 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 ...
515 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 ...
47 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, ...
79 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 ...
59 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?
56 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 ...
67 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 ...
144 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 ...
46 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?
179 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 ...
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 ...
85 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 ...
52 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 ...
87 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 ...
63 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 ...
110 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, ...
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....
54 views

### Vertex positions from particle position

I have a question about Nvidia Flex or any particle based simulation in general: The particles are created by sampling the mesh, which can result in fewer particles than there are vertices in the ...
62 views

### How to scale primitive shapes [in Blender] so that they are within a [unit] sphere?

I wonder how is it possible to scale all shapes so that they are within boundaries of a [unit] sphere? I know how to do this for a cube: if radius of the sphere is S...
207 views

### Do straight lines always remain straight when projected with a perspective camera?

If I have a straight line in 3D space and I use a camera matrix to do a perspective projection into a 2D plane/screen will the resulting line always be straight too? If I project the start point and ...
64 views

### Intersecting Frusta

I am trying to determine whether two frusta intersect in 3D space and to quantify this intersection as a percentage of one frustum volume (eg. 100% intersection meaning that the two frusta occupy the ...
436 views

### Texturing an “infinite” plane

I am rendering an infinite plane as described in the following answers: https://stackoverflow.com/questions/12965161/rendering-infinitely-large-plane https://stackoverflow.com/questions/7380250/how-...
104 views

### How can you avoid thin triangles in a parametric shape in a smart way?

I have created a closed 3D mesh using a parametric function. The shape is constructed by taking an arbitrary closed b-spline and scaling it based on one of the parameters (similar idea to a parametric ...
218 views

### Should you measure mesh complexity in triangles or vertices?

I have seen people using either vertices or triangles as a quick heuristic to estimate mesh memory usage and mesh rendering time. I always thought vertices were better, because the number of vertices ...
1k views

### Why are oct trees so much more common than hash tables?

When reading papers I commonly find Oct tree implementations of geometry representations to sort the data. However whenever I think about the problem hash tables seem better overall. Hash tables have ...
74 views

### Given a picture of a unit square at an arbitrary angle and position, how can I reconstruct the distance and orientation?

To simplify, assume faces and corners of the square are labeled and the camera lens if whatever makes this simplest (a 90 degree field of view projection?) The application: using a known and labeled ...
549 views

### ray-triangle intersection precision - c++

I'm building a software renderer but I think there might be some problem with my ray-triangle intersection accuracy. I implemented the algorithm referring to ...
187 views

### What is the equivalent of rotation matrix in Euler angle space for Quaternions?

I have to load a mesh in Blender (which uses Z and Y as up and forward axes), modify it and export it (with setting up and ...