Questions tagged [mathematics]

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11
votes
0answers
623 views

How correct is rendering in XYZ / linear RGB space?

I have a spectral power distribution (SPD, 5 nm steps) for all light sources in the scene and SPDs for the reflectance of all surfaces under any light / viewer angle in question. I'm going to ...
5
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0answers
178 views

Ray tracing implicit surfaces using Sturm's theorem

I am trying to render implicit surfaces given by a polynomial equation $F(x,y,z) = 0$ using Sturm's theorem. Plugging the parametric ray equation $r(t) = o + td$, where $o\in\mathbb{R}^3$ is the ray ...
4
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3answers
102 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, ...
4
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0answers
165 views

Pre-filtered environment map, deriving the equation

I'm reading through this article, and more specifically I'm trying to derive the equation that would explain the implementation the following shader (still in the same article): ...
4
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0answers
54 views

Making surface with common parametrization from bunch of other surfaces

I have bunch of surfaces, like in these two images: Currently to make single surface with common parametrization I sample points uniformly from all source surfaces, and fit single NURBS surface from ...
3
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0answers
91 views

Procedural Generation of 4D Shapes

I'm curious if anyone has any insight into how one might procedurally generate 4D objects, as showcased in Miegakure (or the developer's other game, 4D Toys ). I built a program a while back to do ...
3
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0answers
49 views

NURBS Weights De Boor's Algorithm

I am having trouble implementing an algorithm for 3rd degree NURBS. I have been able to program 2nd degree ones from the equations described here but I am not able to derive an equation for Rational B-...
3
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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 ...
3
votes
1answer
338 views

How to match Blenders polynomial lens distortion model with GLSL?

I'm trying to re-implement Blenders (libmv) polynomial lens distortion model using shadertoy, in order to apply the lens distortion in another application ideally by generating a STMap for that. I ...
3
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1answer
276 views

Barycentric coordinates for 5-sided polytope of two triangles and three trapezoids

I have a triangle that is extended in space and each edge is refracted differently, creating a 5 sided polytope. The initial and final triangles are the view radii segments of a frustum. We need to ...
3
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0answers
83 views

What is a good algorithm, and framework, to calculate centres of gravity or mass (cog)?

I'd like to take an photograph, subdivide it into a tesselation, either of squares, or (ideally), hexagons, and then find the centre of gravity (or, if you prefer, centre of mass) of each cell of the ...
2
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0answers
47 views

When should operations on 4D (homogeneous/projective) vectors use the w-coordinate?

Various operations on 2D vectors naturally generalise to 3D vectors simply by including the $z$-coordinate. The ones that come to mind are: Vector sum and difference Dot product Magnitude (Euclidean ...
2
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0answers
72 views

Constraining a Polyline to Look Smooth

What are the mathematical constraints required for a polyline, i.e., a piecewise linear curve, to appear as a smooth curve to human vision? I've discovered one document that specifies only that the ...
2
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0answers
166 views

Transform a centered isosceles trapezoid in a rectangle in 2-D

I must convert a isosceles trapezoid to a rectangle in 2-D with a shearing transformation (or with 2 shearing transformations). The isosceles trapezoid is centered in the origin of axes. It is right ...
2
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0answers
57 views

Compute angles and thereby endpoints in a raster grid?

I am at the moment having some issues with computing an endpoint in a raster grid that is also a valid position in a graph. I am trying to draw a line between these two points, but as the point I am ...
1
vote
1answer
21 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 ...
1
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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'...
1
vote
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 ...
1
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0answers
34 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)}{...
1
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0answers
110 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 ...
1
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0answers
74 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-...
1
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0answers
100 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: <...
1
vote
1answer
102 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 ...
1
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1answer
64 views

Estimating the position of vertexes in a 3D model

Introduction to my project: We are machine learning scientists and working on a biomedical system for tracking tongue for speech pathology using a technology called EMA (Electromagnetic ...
1
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0answers
18 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 ...
1
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0answers
163 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 ...
1
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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 ...
1
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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: ...
1
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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 ...
1
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0answers
125 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 ...
1
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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 ...
1
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0answers
643 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 ...
1
vote
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 & ...
0
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0answers
53 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 ...
0
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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 ...
0
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0answers
32 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 ...
0
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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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0answers
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")
0
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1answer
44 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?
0
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0answers
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 ...
0
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0answers
48 views

What library or tool was used to plot these graphs?

I've been wanting to plot graphs that look like these (Taken from this blog post), but I can't figure out what tool, language, or library was used to pull this off.
0
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0answers
182 views

SDF collision detection

I was wondering if there are any techniques for calculating the intersection point/s between two or more distance fields.
0
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0answers
28 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.
0
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1answer
378 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 ...