Questions tagged [mathematics]

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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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0answers
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'...
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0answers
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 ...
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0answers
35 views

What is the projection matrix of reverse (Byzantine) perspective?

I would like to construct a projection matrix for reverse perspective. I'm using OpenGL and tried to modify concepts from this excelent tutorial. I came up with: $$ \begin{bmatrix} 2\frac{(near-M)}{...
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0answers
124 views

Why does Schlick's approximation contain a \$(1-\cos\theta)^5\$ term?

The approximation writes the reflection coefficient as$$R(\theta)=R_0+(1-R_0)(1-\cos\theta)^5,\,R_0=\left(\frac{n_1-n_2}{n_1+n_2}\right)^2.$$Why is the exponent 5? Schlick 1994 introduces this ...
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77 views

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-...
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0answers
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: <...
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1answer
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 ...
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0answers
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 ...
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0answers
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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0answers
37 views

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 ...
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1answer
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 ...
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0answers
68 views

Hashing a point on cubic sphere

Let's say I have a point on a potential cubic sphere inflated using this: ...
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0answers
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. ...
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0answers
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 ...
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0answers
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 ...
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3answers
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 ...
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0answers
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 ...
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0answers
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 ...
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1answer
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 & ...
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1answer
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, ...
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1answer
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 ...
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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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1answer
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 ...
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1answer
111 views

Prove radiance contributions of deeper paths fade away

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 ...
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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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1answer
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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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
77 views

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, ...
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1answer
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?
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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 (...
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1answer
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 ...
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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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0answers
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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0answers
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 ...
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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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0answers
32 views

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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50 views

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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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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1answer
62 views

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 ...
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22 views

GIMP's Additional blending formula

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 ...
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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.
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0answers
29 views

How can I create multivariable function plotting software

I have finished Dennis Ritchie's C book, and I would like to create my own plotting software for enhancing my programming skill,I want sources,books or anything to reach this goal.Thanks for answers.
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1answer
382 views

Translate an arcball camera upwards or left-right

This problem is giving me a really hard time. I'm always looking at the origin and have a camera that moves around it in an arcball mode. That part works beautifully: I'm calculating the camera ...

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