# 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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### 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 ...
1 vote
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 ...
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1 vote
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### 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 ...
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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....
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 ...
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 ...
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 ...
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### 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 ...
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. ...
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### 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 ...
• 1,706
1 vote
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### 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 ...
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### How is re projection usually implemented in remeshing?

I was reading "Polygon Mesh Processing" and in chapter 5 the authors present this little algorithm: ...
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1 vote
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### 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 ...
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/...
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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
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 ...
1 vote
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 $f$ ...
• 111
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, ...
• 127
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: ...
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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 ...
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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 ...
• 1,706
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.
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-...
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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 ...
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1 vote
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### 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 ...
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### 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 ...
1 vote
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
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 ...
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1 vote
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 ...
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### 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 ...
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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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### Is it possible to make a projection matrix to not project in the center?

I have the following projection matrix: and I need to make a hole in the center of my matrix, something like that: (I don't want to project a custom W and H) Is that possible ? Thanks.
1 vote
156 views

### Defining the proper sdf for this structure

I am making a procedural sdf (just a bunch of cubes) based of an image. The idea is very simple. We have a stencil image: Each texel in the image corresponds to a 3D cube. So to ray trace what I am ...
• 1,706
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 ...
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188 views

### physics/math of lighting gradient of a 3D object

Consider a monochrome ball. The colours of the pixels is a function of the point height, the light intensity, the light angle, and the surface material (reflection). What is the simplest formula ...
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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 ...
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