# Tagged Questions

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### Rotate and translate a line so that it passes through two given points

I have 2 point and a line segment in 2d space. The line only rotates and translates using its mid point. How do I calculate the translation and rotation required for the line to be touching the 2 ...
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### Stable equilibrium position of 3d models.

I have 2 models, described by vertices arrays. The aim is to find stable equilibrium position of one of the models upon the other. The algorithm should consider the possibilities of transformation of ...
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### Intersection of two lines in 3D

The two points $A=(x_{0},y_{0},z_{0})$ and $B=(x_{1},y_{1},z_{1})$ are given. I want to find the coordiantes of the point $C=(x,y,z)$. The line segments $AC$ and $BC$ make equal angle $\alpha$ with ...
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### Oblique projection for which the projection vector is at an angle of 45 degrees

dixit: A special case of oblique projection is called cavalier projection. It is given when the projection vector forms an angle of 45° with the z-axis. This means that: $$(x_p^2+y_p^2)/z_p^2=1$$ My ...
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### Translation of basis for a vector space on the specified distance

In the Euclidean space $XYZ$ is a basis $X_1Y_1Z_1$ defined that is specified by the vectors $\overrightarrow {O_1X_1}$, $\overrightarrow {O_1Y_1}$ and $\overrightarrow {O_1Z_1}$. How to calculate ...
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### Intersection between 2 lines (3D). This doesn't have a solution does it?

so I was looking through an old exam and this question was given: The teachers answer was the point (9, -9, 21) I tried solving this myself, I got x = x, y = y, but I could not find a point where ...
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### What is and what are the use for an “ AINV preconditioner ” or “ SAINV ”?

In an article that I'm reading there is a mention to this "thing" and I absolutely don't know anything about it, for me it could be anything. I noticed that this thing is somehow related to the math ...
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### Rotate XYZ frame in 3D space

Given a XYZ frame in 3D space at origin O(0,0,0). And given a plane equation: ...
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### How does a measurement error change the volume of a tetrahedron?

Consider that I have a tetrahedron $T$ whose the lengths of edges are $(a,b,c,d,e,f)$. I want to calculate the volume of the tetrahedron by Cayley-Menger Determinant. However, I know that, the ...
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### Transformation of the points on a plane

How do I transform a point $(x,y,z)$ on plane $\Pi (ax + by + cz = 0)$ to a point $(x',y',z')$ on plane $\Phi(ax+by+cz+d=0)$? What matrix should I use? Here is a 2-D representation of what I'm ...
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### slope of a line in 3D coordinate system

Suppose I have $2$ points in a 3D coordinate space. Say $p_1=(5,5,5)$, $p_2=(1,2,3)$. How do I find the slope of the line joining $p_1$ and $p_2$? After getting the slope (which I assume will be an ...
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### Find point in 3D space based on plane and known point

I'm struggling with drawing geometry in 3D spaces via OpenGL. My current task is to find coordinates of point. Assume we have such input data: Points $a$, $b$ and $k$ define a plane. Point $c$ ...
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### Projecting 3D Point to Plane

I have a plane defined by the equation $Ax + By + Cz + D = 0$. It does not pass through the origin. I have projected the origin of my global coordinate system onto the plane, so it is at $(a, b, c)$. ...
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### Rotating by the pivot point and store the result as rotation by the (0,0,0) + translation.

I have an object in 3D space, but I guess that problem is dimension-independent - you can assume it's 2D as well. I have an object (box) - I store only its ...
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### Vectors to Matrices in algebraic equations

This question is based off of Dave Eberly's 3D Game Engine Design, 2nd Edition. I am reading it slowly to gain a larger algebraic grasp of 3D graphics, which this book seems to offer. When finding a ...
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### Calculating Intersection of Three Spheres Step by Step

How do I calculate the intersection of three spheres step by step? Assume that the spheres are $S_i(c_i, r_i)$ where $i = 1,2,3$, $c_i$ is the center coordinates of $S_i$ and $r_i$ is the radius of ...
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### Normalizing a 3D angle distribution

I'm having trouble finding the proper keywords to search for this type of treatment so I apologize in advance if this is quite obvious. I have a collection of lines in 3D space approximately centered ...
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### Angle between two 3D lines

I know for given 2 vector $\vec{u},\vec{v}$ the angle between them achieved by - $$\cos{\theta} = \frac{\vec{u} \cdot \vec{v}}{\|\mathbf{u}\|\|\mathbf{v}\|}$$ but what if I want to calculate the ...
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### 3D vertices $\rightarrow$ 2D polygon $\rightarrow$ 3d transformation

This may be a little strange. I have an array of 3D vertices, which represent a 3D face (n-gon). I first need to describe the face in 2D. I can then apply these transforms on it. X, Y, and Z ...
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### Getting a 3d linear equation knowing the rotation of an object

I have an object, a simple rectangle I rotate it by a certain degree using Euler Angles, in this case around Z, to make it easy lets say it's 45 degrees. Right now I want the yellow: Y-Axis linear ...