# Questions tagged [geometry]

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### Direct Light Sampling produces way too bright images compared to naive diffuse bounces only

it's me again! :D I have finally implemented area lights, but without modifying the emission value of the material, this is what it looks like with indirect light only, this is what it looks like with ...
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### How to implement camera translation arround object using gluLookAt?

I'm trying to move my camera around the object, a house, using some keyboard keys and the gluLookAt() function. ...
102 views

### Extrapolating geometry across a triangle mesh?

Say you have 2 parametric cylinders represented as triangle meshes with very different geometries and you connect them together. Is there a method that allows you to join them together such that the ...
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1 vote
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### Piecewise smoothing of a mesh?

Kobbelt et al. published a paper some 20 years ago where they specified how solving Poisson equations on the positions of a mesh lead to removing noise. This can be used for reconstructing mesh ...
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### How is re projection usually implemented in remeshing?

I was reading "Polygon Mesh Processing" and in chapter 5 the authors present this little algorithm: ...
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### interpolated normal vectors after tessellation. How to hash patch corner / edge vertices?

I have a 3D geometry (an asteroid) that is to be tessellated with respect to the camera position. Each vertex in the original mesh has a unique position and is stored once (VBO with IBO) In the ...
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### Faring a region of a mesh connecting two curves

In the book Polygon Mesh Processing, there is a section dedicated to fairing. In particular page 59 has this lovely figure: I am specially interested in the rightmost image. According to the text ...
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### What is a smart way to fill in the 'next' pointer of a opposite half-edge of a boundary?

I was reading this question regarding half edges from 3 years ago and the selected answer seemed pretty smart to me. However, while actually implementing it I'm confused at the part where I have to ...
36 views

### How to measure distortion of a parametrization?

If you have a map from a mesh into the 2D plane. How do you measure its distortion? I know that theoretically what you do is express the differential map of the transformation then use SVD to figure ...
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### Volumetric mesh processing: impact of facet removal on connectedness?

I am working with volumetric meshes - meshes that have vertices (0-cell), edges (1-cell), facets (2-cells) and volumes (3-cells) - and I'm interested in removing facets without breaking connectedness. ...
68 views

### What are applications of 3D geometry to 2D geometry projection and occlusion handling?

As a layperson in the field of computer graphics, I rarely see practical applications of algorithms that take 3D geometry as the input (along with some camera and lighting parameters) and output the ...
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### looking for meshlet generation algorithms

I am looking for algorithms to create meshlets from triangulated meshes. I searched for articles, but could not find any. Maybe "meshlet" is not the right term? I want to cluster the faces ...
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### How to extract region inside a loop on sphere

The input is a sphere(defined by radius and center) and a loop defined by a set of points(unordered, illustrated in cyan in the image above) that satisfy the implicit function of the sphere. How can I ...
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### Interpolate Gradients to Vertices of triangular mesh

A well known way of interpolating the gradient field of a scalar field onto faces of a triangular mesh uses the following formula (source: https://www.cs.cmu.edu/~kmcrane/Projects/HeatMethod/...
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### Creating a UV Map for a 3D Cone

I have the following problem I am currently facing. I am creating the vertices for a cone based on the number of segments and the radius of the base and top. This is done as follows: ...
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1 vote
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### How to get the boundary of delaunay triangulation

I'm implementing tunnel detection algorithm in the paper "Computing Geometry-aware Handle and Tunnel Loops in 3D Models". Before the actual tunnel detection, the input needs to be ...
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### Stitching 2 boundaries together

Let us say we have 2 boundaries of 2 meshes that are roughly aligned, for example 2 generalized cylinders (sweeping surfaces) with a small gap in between. And let us say we want to connect them to ...
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### How do algorithmic botany algorithms generate their plant geometry from a skeleton?

I read the Algorithmic Beauty of plants.The resource goes in depth as to how to generate plant topology, but it does not talk about how to make the geometry except for the leaves. I tried looking into ...
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1 vote
330 views

### Clever projection of point onto triangle?

I know of at leas tone way to project a point onto a triangle. Project onto the plane, check barycentric coordinates, if outisde triangle, project onto the 3 segments, check distance, retain closest ...
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### How to create a mesh from a skeleton?

Say you have a topological skeleton, you want to fabricate a mesh out of it, what algorithms exist to accomplish this? I know of at least one way, which is to represent each edge as an implicit ...
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1 vote
63 views

### Inverting perspective projection doesn't yield frustum?

I have a cube with 8 vertices representing the $[-1,1]^3$ cube vulkan uses for device coordinates. The perspective projection matrix takes a frustum and maps it onto this cube. It thus makes sense ...
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1 vote
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### Calculating ray intersection with two spheres (with smooth_blending between the two spheres to make them appear as one continuous geometry)

I have the following function to define the distance to the interesection between a ray and the surface of a sphere: ...
1 vote
41 views

### Geodesic triangle strip algorithm

I think somewhere in the literature there is an algorithm that, given 2 points on a triangle mesh, finds the triangle strip through which the geodesic passes, but I cannot find it anywhere.
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### How can we represent a self-intersecting surface without analytic expression in computer?

Suppose we have a suface without self-intersection, then we can store it numerically using grid samples from its signed distance funtion. But what for the self-intersecting case, can we still use the ...
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### Simulating a moving catheter inside a human heart

I'm trying to simulate a moving catheter inside a human heart. I want to accurately model the behaviour of the catheter and I assume the heart to be solid. What I want is, when the catheter hits the ...
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### What stops the auto-generated 3D worlds of Google Earth Pro from being MUCH more detailed and accurate?

I'll admit it blew my mind when I first realized that you could actually enter a "first-person mode" in Google Earth Pro, and not just view the 3D maps from a floating camera in the air. But ...
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### How to delete a face using open mesh?

Pretty much the title I am trying to delete a few faces of a mesh using open mesh, like this: ...
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### Student-friendly ray-triangle intersection

I'm teaching a computer graphics course, and would like to give my students a function for calculating ray-triangle intersections (not just the point of intersection, but also the uv coordinates ...
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### What's a simple way to find connected components in a mesh?

As stated I have a triangle mesh I want to separate into connected components. One way I would assume would be to do a depth first search on a vertex and remove vertices, then repeat until the set is ...
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1 vote
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### Geodesic approximation algorithms for minimal geodesic curvature

Introduction I am building an application in which given a surface and a pair of points on it, an analytic expression of some geodesic arc (preferably the one with the shortest length), between them ...
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### When fitting 3d cuboids into a box, how to find the order of drawing (in a 2D projection) so that the cuboids don't appear to overlap?

I am working on a 3D packing algorithm (MIT-licensed). The box and the cuboids it contains are displayed as a 2D projection. The order of drawing the cuboids (now represented as polygons) is important:...
1 vote
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### Extrude from line and find intersection points

Hey Im currently learning about geometry and vectors and was trying to build a room builder with three js. I basicly create walls from two points (p1, p2). I draw a line and extrude the line to a ...
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### Which provides better intuition: THREE.Geometry or THREE.BufferGeometry?

THREE.js recently dropped support for THREE.Geometry in favor of exclusively THREE.BufferGeometry. I'm trying to decide which paradigm to teach in my computer graphics course to best provide students ...
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### $(x, y, 1)$ is 2D homogenous coordinates or 3D homogenous coordinates?

We know that $(x, y, 1)$ are the homogenous coordinates of a 2D point $(x, y)$. $(x, y, 1)$ has 2 degrees of freedom. That's why we should call it 2D homogenous coordinates. But many websites say it's ...
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### Finding a texture pixel (X,Y) on a Sphere

I'm using three.js combined with face recognition, I want to rotate a sphere that displays my input video according to the detected eye location, the face recognition gives me a X,Y on the texture ...
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1 vote
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### Half Edge criterion to check if an edge flip is illegal?

I am trying to determine if and when flipping an edge is topologically valid. The current criterion I have is that it is only valid if there is no edge connecting the opposite vertices of the edge. I....
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1 vote
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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 ...
1 vote
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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 ...
146 views

### 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 "...
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1 vote
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### 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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### 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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1 vote
151 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 ...
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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,...
53 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 ...
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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 ...