Questions tagged [geometry]

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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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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 ...
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2answers
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 ...
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1answer
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 ...
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1answer
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 ...
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1answer
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 ...
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1answer
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 ...
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1answer
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 ...
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1answer
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 ...
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2answers
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 ...
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2answers
61 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 ...
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2answers
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 ...
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1answer
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 ...
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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 ...
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1answer
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 ...
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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 ...
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1answer
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 ...
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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==...
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1answer
48 views

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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1answer
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, &...
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2answers
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 ...
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1answer
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 ...
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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, ...
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1answer
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 ...
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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?
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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 ...
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1answer
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 ...
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2answers
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 ...
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1answer
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?
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2answers
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 ...
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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 ...
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1answer
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 ...
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1answer
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 ...
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1answer
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 ...
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0answers
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 ...
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3answers
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, ...
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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....
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0answers
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 ...
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1answer
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...
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1answer
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 ...
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0answers
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 ...
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1answer
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-...
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0answers
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 ...
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2answers
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 ...
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2answers
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 ...
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1answer
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 ...
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0answers
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 ...
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1answer
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 ...
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1answer
73 views

How to rotate a shape in another 3D software so that the rotation matches with the rotation in Blender?

I import a mesh in Blender, export it with setting axis_forward='-Z', axis_up='Y', import in NVIDIA's FleX, rotate it and store it on disk; I call this mesh ...
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1answer
9k views

How to convert Euler angles to Quaternions and get the same Euler angles back from Quaternions?

I am rotating n 3D shape using Euler angles in the order of XYZ meaning that the object is first rotated along the X axis, then Y...