Computer Graphics Stack Exchange
Computer Graphics Stack Exchange

Questions tagged [computational-geometry]

Problems involving meshes and other geometry representations, and manipulating, transforming, or extracting information from them; algorithms for solving geometrical problems such as computing intersections, filling holes, triangulating a shape, etc.

Computational geometry encompasses a wide variety of topics, including:

  • Modeling surfaces and solids using meshes, splines, and other geometry representations
  • Generating geometry from implicit or parametric functions, point sets, or other data
  • Processing geometry to extract information about orientation, topology, curvature, or other quantities
  • Performing operations on geometry such as tessellation or triangulation, simplification, CSG operations, feature extraction, UV mapping, and cleaning up mesh errors
204 questions
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Two-dimensional bounded area defined parametrically

How do I go about defining this area without using a piecewise function? I think it has something to do with Bilinear Surfaces but I'm not sure how to get started.
Gavin
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5
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1 answer

Topological Sweep

I need to identify certain topological entities (circular holes) in a given geometry, that is, given the boundary representation of a solid, I need to identify the exact coordinates of all holes in the solid. I have been told to use a topological…
jcp1966
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5
votes
1 answer

Closed form solution to a problem of tangent circles

I have two circles, that I know are both tangential to a third (unknown) circle. I also know what quadrants of the circles the tangential points are in. It is as pictured below. I also know the arc angle that the third circle spans between the two…
Rikki-Tikki-Tavi
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5
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1 answer

Identify different contour cycle after model slicing

The slicing algorithm is done on the STL model and it is ensured that the result is a series of simple polygons that do not intersect each other. In other words all of those polygons generate closed loops. I need to identify which of those loops are…
sajis997
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5
votes
1 answer

generate multiple border contour

Once a 3D model is sliced against a plane and projected onto it, we get a contour curve at certain height. The contour curve I am generating in this process is made of several line segments in closed loop. Now I want to generate another contour…
sajis997
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4
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2 answers

How to describe a position of a point w.r.t the position and orientation of 3 other points

Is it possible to describe a position of a point $A$ (in 3D) w.r.t. the position and orientation of 3 other points? If so, how? FYI, the 3 other points lie on a plane, whereas the point $A$ is not on the plane. Just to elaborate, initially I have…
Bla...
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4
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0 answers

Algorithm to remove inner faces of a triangulated mesh

I'm trying to figure out the surface area of a mesh that is the result of various CSG union operations between an arbitrary number of other meshes by summing up the same property of each one of it's faces (triangles, in this case) but the result is…
Liordino Neto
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4
votes
3 answers

Fill the plane with pentagons as tightly as possible in a regular way

I wrote a small python script with recursion to create a "lattice" of non-overlapping pentagons. Below one can see the first stages of recursion. One can see that 5 small pentagons are missing in the second stage of recursion. The code in python…
minimax
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4
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1 answer

How to project a 3D point onto a plane along another (axis) vector?

I have a point $P = (0, y, z)$. I need to determine the $x$ coordinate of its projection $P'$ onto a plane $T$ along the $x$ axis unit vector $\vec{X} = (1, 0, 0)$. The plane $T$ is defined by a point $V$ that lies on $T$ and its normal $\vec{N}$…
niksbenik
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4
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2 answers

I need advice and good reference in geometric modeling?

I am a student of computer science and this semester is my first semester of MSc. Next semester I must choose an advisor and the subject of my dissertation. I somewhat know what geometric modeling is and I want to research in this area, but I don't…
haleh
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3
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1 answer

Given two arbitrary surfaces, what is the accurate and quite fast algo to find collision within X distance?

I have two high-resolution 3D objects(femur and patella) with arbitrary smooth surface and I want to find the contact point/area between those two objects. Accuracy is more important than computation time in this case, though it would be great if…
Bla...
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3
votes
1 answer

Efficiently generating mesh for self-generated voxel grid

I'm working on an app that lets users construct a 3D house, with the ultimate goal of it being 3D printable. I use various materials in the form of a height map constructed from an image, like this brick texture: I map the brightness of each pixel…
andygeers
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2
votes
1 answer

Volume of Intersection of Cube and Sphere

Is there any way to compute the volume when a sphere intersects a AABB(cube), with different centers. Also i want to be able given a percentage of sphere's volume to to place the sphere's center in a point in 3D space where it intersects the AABB…
Code Master
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2
votes
1 answer

Camera rotation effect on pitch, yaw, roll

I'm trying to calculate what the effective pitch, yaw, and roll are for an image. I have the image's original pitch, yaw, and roll. Then the image (camera) is rolled at some arbitrary angle. I want to calculate the new relative pitch, yaw, and…
user657
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2
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0 answers

How to find the major and minor axes of a convex hull?

I have a set of particles in a gravitationally bound system. The shape of the particles change with time, I have used a convex hull algorithm to "enclose" the particles of the cloud. I want to find the major and the minor axes of the cloud. hulls =…
Penguin1068
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