Questions tagged [vectors]
The vectors tag has no usage guidance.
42 questions
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Projecting Vectors (3D to 2D) Using Homogeneous Coordinates, With Known Camera Calibration
Suppose I have vectors in a 3D space (their starting points, dx, dy, and dz), and I would like to project them onto a camera, which I already have as a 3x4 projection matrix.
I can of course project ...
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2
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How are surface normals dealt with in the graphics pipeline?
I know the process for regular vertices is something like: model coordinates to clip space via the "MVP" matrix transformation, then perspective division, screen-space mapping, and finally ...
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What to do with the homogeneous $w$ during vector operations
As I understand it: In graphics, 3D vectors are usually represented as homogeneous coordinates by storing an additional $w$ component known as the weight. The vector is divided by $w$ to obtain the ...
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Environment map: inverting (phi, theta) to (x,y,z) mapping
I'm currently working on a ray tracer in C++ as an assignment. This ray tracer needs to take into account environment maps, which I also need to implement a part of. From my understanding of an ...
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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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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 ...
- 1,366
2
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1
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126
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Trouble transforming vectors from view space to screen space using a perspective projection matrix
I can't for the life of me figure out how to use a perspective projection matrix. My understanding is that, once objects are in view space, the the perspective transform uses the z-coordinate to ...
- 1,366
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Split a string of line segments into several other line segments
I have written a code to extend "n" points, constituting "n-1" lines ,to constitute more lines so you can map "m" data to "m" lines with m > n-1.
This is the ...
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Mathematical foundations of Signed Distance Fields in computer graphics
I have come across Signed Distance Field usage in Computer Graphics in construction of vector shapes, glyphs and 3D surfaces. However I can not find much of the background mathematical theory as to ...
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Help understanding tangent from dot product and max distance from component wise vector multiplication
I am looking through this code and seeing two things which confuse me (well, the whole functions does) in the top functions.
First, dir * p where ...
- 3,484
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Plotting points along a 3D line segment
I'm trying to plot some points along a 3D line segment and could really use some help. In 2D, I've found success getting the angle of the line, the sine & cosine of the angle, and then adding the ...
- 2,232
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How do I figure rotation from the difference between two vectors?
I've been playing around with an idea, but I'm struggling with some of the math involved.
Now, each face of a mesh has a normal vector, and that the normal map fragment shader modifies that face ...
- 101
3
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1
answer
826
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Video-games; Rendering textures on scope zoom-in. Texture compression problem?
This is general question.
In the multitude of video-games that are not specialized in scoped warfare (like Sniper Elite), I've noticed that when you zoom in with a scope, the textures and normal maps ...
- 133
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Crystal ball rotation - I don't get why the code works
For context:
I'm absolutely new to graphics programming and I've always had trouble getting the math.
I had the task to write code for a crystal ball interface using OpenGL.
There's an object in the ...
CommunityBot
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1
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Extending an orthogonal set of vectors (graphics application?)
Sorry if this is OT, but I'm wondering if there's a specific graphics technique in which it is required to extend a preexisting orthogonal set of vectors (not necessarily to a full basis, but perhaps ...
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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")
2
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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 ...
- 121
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2
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131
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3d Math Primer book equation derivation - Projecting One vector onto another
I'm reading the book 3d Math Primer for Graphics and Game Development 1st edition by Fletcher Dunn and Ian Parberry. On page 61 there's this:
How does it derive $ v_{||} $ there? It doesn't follow ...
- 2,561
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1
answer
679
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Calculating the angle between two polygons
For my application, I want to render models as polygonal surfaces in 3D space and have edges that are bent "outwards" to have a solid line and those who are bent "inwards" to have a dotted line. So if ...
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Application of parallel transport in computer graphics and mesh processing
Does anyone know what applications has the computation of a parallel transport on a mesh?
I'm talking about methods such as this one
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1
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Finding the normals of a tileable 2D surface extracted from 4D space
If I use a 4D noise function which returns a noise value and a four-part analytically derived gradient vector, I can create a 2D tile which is seamless (i.e. the opposite edges match) through ...
- 2,561
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1
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135
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How do I derive this transformation
If I had two right handed frames where one has vectors [i, j, k] and another with corresponding vectors [u v w], how would I derive the transform M[i j k] <-- [u v w] when applied to any point P in ...
CommunityBot
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1
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215
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Morph Targets Normal adding math
I am trying to verify that if I have my inNormal and some N amount of morph normals that I would want to do something such as
<...
CommunityBot
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3
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801
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Rotation of a random unit vector at a point in 3D space by an angle
I have a scenario where I need rotate a vector ( unit vector) at a point in space by an angle along Z-axis. Is it possible to help me to understand a procedure to achieve this. I'm using vb.net ...
CommunityBot
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5
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2
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169
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Refraction: given an incoming and transmitted direction, can I deduce the normal?
It's easy to find guides to calculating the transmitted direction of light given an incoming direction, the normal, and indexes of refraction. However, I can't find anything about determining the ...
- 1,585
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1
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635
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Vector Math for Raytracer
So i am working through the book "Raytracing in one weekend".
At the point where i am at we want to check if a ray hits a sphere.
For that we have the equation:
...
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0
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164
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Basis vectors and plane equation
I'm trying to understand basis vectors and the plane equation and I am confused. From what I saw, if we take a basis vector i, j, k, each variable point to the axe (x, y, z). Are i,j,k scalars or ...
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1
answer
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Perlin Noise with Smooth function vs Lerp
I tried implementing Perlin Noise using the Wikipedia as my main resource. From what I can tell my implementation of the ...
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2
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1
answer
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Creating vector shapes using only C++ [closed]
I've been researching for quite a while and I couldn't find any explanation or at least a how to create a vector graphic application (specifically in windows) where I can create a 3D vector shape, say ...
- 491
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2
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Can somebody explain this Ray Tracing Function?
I am currently reading through Peter Shirley's Ray Tracing in One Weekend. In the beginning chapters where the author introduces diffuse surfaces we a presented with this function:
...
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What is the difference between a point transformation and a vector transformation?
This is what my lecturer told me in the coursework:
We only consider 4*4 matrices. These are used to rotate, scale or translate objects (or any combination of these operations). Matrices are also ...
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Normal vector in Phong Illumination Model should be normalized?
I'm studying Illumination subject these days and I was given a problem which asks to calculate the intensity using phong illumination model. I'm little bit confused whether I should calculate normal ...
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Where should I project a polygon corner when it is behind me?
I am creating a simple 3D engine as a learning project to get the hang on spherical trigonometry. I am using the following approach.
1. A model consists of a lot of triangular faces.
2. Each triangle ...
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1
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How can I draw a tube on basis of position and angle between two 3d points?
I'm struggling with this idea of creating two particles in 3d and draw a tube between them. I can't figure out how to properly set the angle of the tube. I've used two approaches:
calculating the ...
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0
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Represent vector with arrow
Another code review question.
I am trying to draw an arrow to represent a vector. I have started with an unit arrow with vertices defined as follows:
...
CommunityBot
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2
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intersection between line segments - narrowed precondition
I believe that the issue may already have been discussed here. I want to find if two line segments does intersect and if they do then find and store and intesection points. Now it is already confirmed ...
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Get vector length with GLM
I am quite confused over how GLM library is behaving or I am using it improperly.
glm::vec2 testVec(6,-4);
float len = testVec.length();
I get the value ...
- 2,730
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1
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Test if a point is on a line segment
I have a line segment defined by two end points. And I have another randomly chosen third point and I want to find out if the third point is on the line segment or not. By "On the line segment", I ...
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Interpolating vectors on a grid
If you have values on a grid and you want to find the value of a point within one of the cells, you can use techniques like bilinear or bicubic interpolation to get the data at that point.
What ...
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2
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Correct view-space transform
I am attempting to model a simple graphics pipeline (i.e. Local->Word->View->Screen->2D spaces).
I've been looking at the algorithm required to transform from world to view-space and using the ...
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2
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Ray tracing with thin lens camera
I'm reading Cook's paper "Stochastic Sampling and Distributed Ray Tracing", I don't understand how the rays are generated. He says:
Determine the focal point by constructing a ray from the eye ...
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1
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Graphics Pipeline: Viewspace & Back face culling incorrectly
I'm attempting to model a simple graphics pipeline - using Matlab at the moment as a modelling tool to get the transformations correct. I appreciate there are software tools that would make this ...
