# Questions tagged [mathematics]

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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 ...
23 views

### Finding a flat plane within iPhone depth data

I have real time depth data coming from an iPhone and I want to identify flat objects within the point cloud so that I can highlight the Hard edges in the images. The objects can be at any angle and I'...
78 views

### Why does my self-written rendering engine make further away objects look larger?

I am writing a very simple rendering engine. I have already made a few tests, but somehow the images it creates look wrong. Objects that are further away from the camera look larger than objects ...
35 views

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### GPU Procedural placement - Creating evenly distributed sampling points

I am working on a procedural placement system on the GPU, inspired by the work done by Guerrilla Games in Horizon Zero Dawn: https://www.guerrilla-games.com/read/gpu-based-procedural-placement-in-...
108 views

### Why does the reflected component in Lambertian path tracing get multiplied by a factor of 2?

I would like to intuitively understand the Path Tracing equation/formula/pseudocode, but I'm not fully getting the last return statement. As per Wikipedia page: <...
131 views

### Camera Implementation without Limitations

I've developed a simple (Third-Person) Perspective Camera with Orbit controls. However, my implementation doesn't handle the case where if the pitch goes over 90º it flips upside down. From what I've ...
19 views

### How can I detect if an edge has flipped during the UV unfold process?

I'm writing my own UV Unfold operation (similar to Maya's Optimize UV tool or 3DS Max's Relax Tool). My code works great 90% of the time but in some instances, I'm getting faces and edges that flip ...
171 views

### Help with understanding the look-at function (the view matrix)

I've been reading this article about the look-at function. I don't understand the part when they're trying to inverse the matrix N. They say that R is orthogonal because all its row and column ...
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### Algorithm for randomly generating polyhedrons?

I want to randomly generate polyhedrons which need not be convex. What is the most efficient way for doing so? I can think of an algorithm for generating random convex polyhedrons, but am unable to ...
147 views

### Wrong tangential directions for cubic bezier curve

I am well aware that there are several ways to find the tangents to a Bezier curve. However, I choose to just substitute the result of differentiating the Bezier curve equation. So, given four ...
68 views

### Hashing a point on cubic sphere

Let's say I have a point on a potential cubic sphere inflated using this: ...
90 views

### How to derive the formula@NathanReed answer [duplicate]

Thanks! A very simple but great way to estimate mean curvatures@NathanReed answer. For my case, I also need an estimate of triangular mesh curvature, and I support this is what i was looking for. ...
104 views

### Round Box SDF scaling issue

I am using the Inigo Quilez SDF function to generate a round box shape. The aim is to be able to control the shape scale, smoothness and roundness. I've achieved a pretty good result but I am facing ...
130 views

### Algorithm for clipping convex quadrilaterals

I'm dealing with hardware that uses quads as its polygonal primitive. Not triangles. A triangle can be expressed by setting 2 of the 4 vertices equal to each other for a degenerate quad. For the 3D ...
491 views

### Return x; y; coordinates of vertex C of triangle

I would like to return the XY coordinates of vertex C using math formula. I have 5 input data what I always know and can be used for solution (green in the image): I know X; Y; coordinates of point A ...
83 views

### Image cleaning - removing all regular shapes ( circles, squares, text, icons etc. )

I'd like an automatic method to clean images. I've been looking at the GIMP, and its command line (cli) interface, in scheme / lisp. It looks very promising, but I'm a complete novice, so I'd be ...
660 views

### Line segment intersection test and find the point of intersection

Thanks for the suggestions. Now I am doing it as follows: First off it is identified if two line segments intersect or not. And I am using the algorithm described in the book - "Introduction to ...
43 views

### Mapping sample to a disk

So I have been reading this wonderful book on ray tracing by Kevin Suffern, Ray tracing from Ground Up. I am reading this book after finishing Peter Shirley's first two book on ray tracing & ...
92 views

### Want to study computer graphics

I want to study computer graphics but I don't have a strong foundation in mathematics. I am doing a computer science degree that doesn't cover computer vision, image processing or computer graphics, ...
146 views

### BRDF ray directions

The BRDF takes two directions, $\omega_{o}$ and $\omega_{i}$. I've heard that both directions should point away from the surface (one towards the camera, one towards the light), but iq's Oren-Nayar ...
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 ...
39 views

### Closest sphere on segment

I am trying to get a segment closest point on a surface and display a circle (or sphere in this case) at that position. I actually get the correct position but I can't get a uniform sphere based on ...
111 views

When ray tracing, I find it intuitively clear that deeper paths have a lower contribution to the overal picture than shorter paths. This is the main reason why it is generally okay to render a picture ...
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 ...
144 views

### Confusion around Lambert's Cosine Law in Ray Tracing in One Weekend

Peter Shirely's Ray Tracing in One Weekend presents the following function to calculate the color of a lambertian material (See chapter's 7 and 8): ...
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### 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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### How are the three plane equations derived in the NVIDIA's CG Tutorial chapter 8?

I'm reading the chapter 8 of the Cg tutorial and I could not understand 8.4.1 : Because all these coordinates lie in the plane of the same triangle, it is possible to derive plane equations for x, y, ...
214 views

### How to compute volume of intersection of non-axis-aligned cuboids in 3D?

Given two cuboids in 3D space (8 vertex coordinates each) that are arbitrarily oriented, how can we find the volume of overlap between them in the fastest manner?
27 views

### Explanation of converting a look-at / direction vector to quaternion rotation?

Can someone please explain the math behind converting a direction-vector or lookAt-vector into a quaternion rotation? What I am trying to do? I am trying to create a custom aim-constraint for a DCC (...
28 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 ...
54 views

### Calculating of vectors in Phong Lighting Model

I'm learning about computer graphics and I have some questions about calculation of the vectors, so I will write the exercises that I have and I hope that someone can help me with the formulas that I ...
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### 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 ...
34 views

### Are there algorithms besides Canny edge detection that can create consistent width edges?

Sobel edge detection is pretty much the quintessential way to get edges out of an image. It however suffers from certain quirks. One example is, because it's gradient, based certain surfaces exhibit ...
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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### What are some uses for the vector triple product in computer graphics?

I have just learned about the vector triple product (Lagrange formula) from a math for computer graphics textbook, however the book does not mention any use cases for it beyond the fact that it's a ...
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### Mathematics in Computer Graphics

Can you please recommend some topic for research work related to mathematics in CG? (Maybe something like "Affine transformations in CG")
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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?
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### Wrong reflection

Here is a youtube video showing my problem: youtube.com/watch?v=y8J7VhS2pkM I think I'm either doing the texture lookup on the reflection texture wrong, or the reflection or view matrix is somehow ...
22 views

I try to implement GIMP's the Additional blending mode for layers in my application. I've found the formula: E = min((M+I), 255) I think, that if I blend ...
195 views

### SDF collision detection

I was wondering if there are any techniques for calculating the intersection point/s between two or more distance fields.