Questions tagged [mathematics]

The knowledge of the numbers, formulas, shapes and quantities. In the computer graphics, almost exclusively linear algebra is being used.

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3 answers
385 views

What projection matrix and world transformation do I need to have an isometric projection?

I'm doing my own engine in college to display a wireframe on screen with an isometric projection but I literally can't find any literature about maths behind doing it by hand just for game engines ...
0 votes
0 answers
18 views

How to morph a enclosing mesh according to the enclosed mesh?

I am quite new to meshing and mesh manipulation. I am working on a problem consiting of meshes $A$, $B$, and $C$. The mesh $C$ completely encloses the meshes $A$ and $B$ as shown in the attached ...
7 votes
1 answer
696 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 ...
2 votes
1 answer
202 views

View rotation matrix

Im unsure about how I could describe what im trying to achieve in few words or a title so ill go on to describe it. So I have voxel, in 3D space, represented solely by its center. The voxel though, is ...
0 votes
1 answer
145 views

Point a normal vector towards a point in 3D-Space

Given a normal vector in 3D-Space, how can I rotate the vector, such it points to a point in 3D-Space. I tried couple of ways doing this, which ended up looking completely wrong.
3 votes
3 answers
229 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 articulography)...
1 vote
1 answer
61 views

Measure (or Jacobian) conversion for direction sampling

If in the path tracing use case, I have some sampling strategies to sample a scattering direction in a 2D space ($\theta, \phi$). Of course, I need to convert it to a 3D direction vector (with length ...
0 votes
1 answer
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 ...
1 vote
1 answer
33 views

How to determine the transformation matrix from given initial and transformed co-ordinates?

How to determine transformation matrix for an object given a graph? This is a problem indeed similar to this one. And I've approached it in the same way like there. Given: A line AB A(0,0),B(1,1). It ...
2 votes
1 answer
129 views

How can I determine ideal NURBS surface control points for a multi-patch sphere?

I would like to know how to "parameterize" the control points for the 6 faces of the commonly used NURBS mutli-patch sphere ("Cobb sphere"), for an arbitrary-size control point ...
0 votes
1 answer
136 views

Plot inverse of emulated double-precision floats

I need to accurately plot a line chart using WebGL. The numbers have a precision of around 33 bits - that's too many to fit into a single-precision float's mantissa. WebGL does not support the double-...
4 votes
2 answers
301 views

Degree for Computer Graphics : Computer Science or Mathematics?

I want to learn graphics on a lower level but I have no clue where to start. I know that I will need some hard mathematics (linear algebra, vectors, matrices, transformations...) rooted inside my head....
0 votes
1 answer
54 views

What are the exact math steps to convert sRGB (D65) to Lab (D50) colorspace?

I've been struggling to implement the correct steps (matrices, white-points, etc) to convert some sRGB (RGB) values (already in 0-1 range) to Lab/CIELAB color space. I've tried following guides on ...
4 votes
2 answers
436 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 ...
0 votes
0 answers
40 views

GLSL reflect function math correct?

In the documentation of GLSL - reflect given a surface normal $N$ and an incident vector $I$ the calculation being performed is reported as $$ \text{reflect}(I,N) = I - 2\text{dot}(I,N)N $$ I wonder ...
0 votes
0 answers
47 views

Pixilate/Quantize UV coordinates in world space?

The effect I'm trying to achieve is to have it so that the texture is pixilated/quantized, but the "grid," stays aligned to world coordinates even as the object with it's own UV coordinates ...
2 votes
3 answers
2k views

vulkan perspective matrix vs opengl perspective matrix

Hi I have a slight confusion in using the opengl perspective matrix in vulkan. glm's perspective matrix works directly in vulkan just by multiplying the "[1,1 term by -1 but when I compared the ...
2 votes
1 answer
56 views

value range in CIEXYZ space

When converting from sRGB to CIEXYZ I seem to be off by a factor of 100 I'm trying to convert from sRGB to CIELAB. Calculation First I need to go from sRGB to CIEXYZ. Using this formula I get i.e. ...
1 vote
1 answer
69 views

Confusion regarding incident direction in render equation

I am studying from pbrt-v3 and the rendering equation has just been introduced as $$ \underbrace{L_\mathrm{o}(\mathrm{p},\omega_\mathrm{o})}_\text{Outgoing radiance }=\underbrace{L_\mathrm{e}(\mathrm{...
1 vote
0 answers
59 views

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 ...
0 votes
0 answers
20 views

How is re projection usually implemented in remeshing?

I was reading "Polygon Mesh Processing" and in chapter 5 the authors present this little algorithm: ...
0 votes
1 answer
84 views

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 ...
0 votes
1 answer
64 views

Does CMYK values provide more colors than RGB?

We know that in the RGB system we have three primary colors and each of them has a value from $0$ to $255$ (or $256$ values in total). So all possible colors are $256^{3}=16777216$. But in the CMYK ...
1 vote
1 answer
58 views

Need help understanding this simplification/optimization for a very basic GLSL shader

i'm currently following a tutorial on youtube to get started with computer graphics (shaders) and it contains the following GLSL code: ...
1 vote
1 answer
37 views

Sampling scattering direction around directions other than the last ray direction

In a path tracer, if we want to sample a ray direction in scattering medium, we can use phase function sampling, which actually use the direction of the ray before sampling as a sort of anchor to ...
0 votes
1 answer
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 ...
1 vote
1 answer
58 views

Confusion about the bias during Monte Carlo integration

I recently stumbled into this question: Say, for example, we are doing mean-free-path sampling (distance sampling) in a scattering medium and to keep it simple, let's only consider the single ...
0 votes
2 answers
44 views

Finding vertices of a polytope?

Assume that in 3D we have a polytope defined by the intersection of halfspaces. A half space is the set of all solutions of a linear inequality $P = N \cdot x + c \leq 0$ Where $N$ is the normal to ...
1 vote
0 answers
50 views

Measure for volumetric rendering equation

Recently I've been digging deeper into the volumetric rendering (volumetric path tracing, to be specific). I already know that for surface rendering, there are two commonly used measures (reference ...
2 votes
2 answers
648 views

Discrete Gradient?

I am trying to understand how to get the discrete gradient of a mesh that is being used as the input of some function $f$. In other words for every vertex $v$ there is a scalar quantity $s$ associated ...
2 votes
0 answers
46 views

How to properly use scattering coefficient during volumetric path tracing?

The increased radiance during sampling is known by: $$ L_s = L_e + \sigma_s \int p(w, w')f_p(w, w')dw' $$ The latter part, which accounts for in-scattering radiance bears a $\sigma_s$ in it. The ...
0 votes
0 answers
127 views

One-sample model Multiple Importance Sampling with balance heuristic

Recently I feel a bit confused about one-sample model MIS. One sample model MIS can be found here in Veach 1997. 9.2.4 The one-sample model, and this one-sample model is widely used in the opensource ...
0 votes
2 answers
137 views

Where does sin(theta) go in estimators of The Rendering Equation?

Consider this equation, where we have a surface integral over hemisphere with Lambertian BRDF and cos(theta) from The Rendering Equation: $$ \int_{0}^{2\pi}\int_{0}^{\frac{\pi}{2}}\frac{albedo}{\pi}...
0 votes
1 answer
97 views

With a light source at (0,2,0) and unit cube (from [-1,1]) using a given shading formula, how is the r,g,b for each surface calculated?

The above problem is from a past Computer Graphics exam. I am particularly confused about the explanation given, firstly for the top and bottom planes (since the direction of normal for top plane ...
0 votes
0 answers
73 views

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/...
0 votes
1 answer
164 views

Parametric equation for Catenary curve between two Points

I have two points in 3D space, A and B. I need to have a parametric equation of the catenary curve such that: Cat(0) = A, Cat(1) = B, Cat(t)= f(t, A, B) How can I derive the function f
0 votes
2 answers
216 views

Whats the best way to render (2D) parametric curves with uniform stroke width?

I want to create a rendering engine that mostly renders parametric curves on a 2d screen. As far as it seems, todays graphics are all dependent on vertices and matrices, so not sure where to start or ...
0 votes
1 answer
137 views

Error in equation 2.1. in Ray Tracing Volume Densities

I am reading through Kajiya - Ray Tracing Volume Densities paper. And I've already got stuck into section 2. I wonder if there's a mistake in that equation. I'll quote the relevant bit The quantity ...
1 vote
1 answer
128 views

How to compute discrete partial derivatives in 3D

I'm supposed to compute partial derivatives for 3D volume rendering (in ray tracing). I'm bad at math and so I can't understand what $f$ is in my case. In reviewing examples, I'm seeing the $f$ ...
0 votes
1 answer
144 views

Splitting Floats To Texture Channels

I know, this is a silly question, but since I need this so often, I just want to double check that I made no mistake. Working with most shader languages, a texture can store $8$ bits per channels, ...
4 votes
2 answers
682 views

Can you explain to me the Bresenham's line algorithm in simple terms?

I've been trying to wrap my head around this algorithm, and I need it for my drawing function. But I can't seem to understand it. The Wikipedia page gives this piece of code right at the end: ...
3 votes
2 answers
552 views

Fake cubic Hermite spline interpolation with smoothstep

When scaling an image with Bicubic Interpolation, the Cubic Hermite spline interpolation is used. smoothstep is one of the four basis/blend functions of this kind ...
2 votes
1 answer
40 views

Approximate compass bearing of a normal

Let's say I have a 3D model that represents a small real-world space; it could be bounded by a 10" by 10" by 10" box. I know the real-world compass bearing for an observer in the center ...
2 votes
1 answer
161 views

Can you encode a reflection in a quaternion?

Say we have the transformation: \begin{bmatrix} 1 & 0 & 0\\ 0 & 0 & 1\\ 0 & 1 & 0\\ \end{bmatrix} i.e. the matrix that encodes swapping the z and y axes. This is equivalent to ...
0 votes
0 answers
19 views

Automate Image resize, scale, position for best quality (size)

I have a process where a web user selects a photo for a profile image. User is then presented with a canvas to zoom, rotate and move their image within a square viewport. Once satisfied, the user ...
1 vote
1 answer
54 views

How do I convert pathtraced distance to value that is usable by OpenGL's depthbuffer?

I was hoping someone could check my understanding. I've got a pipeline that does some path tracing, and then draws some debugging rays using standard rasterization. I'm trying to get depth to work ...
1 vote
2 answers
643 views

How to determine transformation matrix for an object given a graph?

I am given this image: and asked to determine the transformation matrix that took me from ΑΒΓΔΕ(let's call it ABCDE for convenience) to Α'Β'Γ'Δ'Ε' (A'B'C'D'E'). I am also given the solution, so as to ...
1 vote
1 answer
103 views

3D to view plane projection

I am trying to draw points of a 3D sphere onto my monitor as if I was looking out into space. Me, the viewer, is at (0, 0, 0). The plane of my monitor is at (x, y, 1) and I have a sphere out in ...
0 votes
0 answers
121 views

Converting a Bezier Path with variable width stroke to an outline?

I started working on a "stylus annotation program", and as part of it I need an algorithm that convert a path with width indicators to an outline. This is similar to the Advanced Outline ...
0 votes
0 answers
51 views

Getting something close to the convex full of SDFs using CSG operations

Inigo Quilez has an explanation of smooth operations to join sdfs. I am trying to get something close to the convex hull of multiple sdfs. For starters let;s consider a simple case of 3 cubes int eh ...

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