# Tagged Questions

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### Is it possible to accurately calculate an irregularly shaped frustum's volume?

I have the following water basin Now imagine this basin is filled with water to the top, is there anyway to accurately calculate the volume of water stored in it using only top and bottom areas A1 ...
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### Counting points in/on cuboid

Given a cuboid that extend in x,y,z axis such that |x|≤N, |y|≤N, |z|≤N where N is given and can have value up to 10^9.Now a shooter is standing at origin (0,0,0).He need to shoot on any of the ...
2answers
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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 ...
1answer
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### Surface of 3D Triangle

The coordinates $A(-1,0,2), B(2,-1,3)$ and $C(4,0,1)$ are the corners in the triangle $ABC$. a) Find the length of the sides in the triangle. b) Find the area of the triangle. Now I'm able to ...
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### Is it possible to create a volumetric object which has a circle, a square and an equilateral triangle as orthogonal profiles?

This question was posed to me by a friend (formulated as creating a peg to fit perfectly into holes of these shapes), and after an experiment in OpenSCAD it seems it is not possible - either one ...
0answers
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### Calculating the length of a NURBS curve

I'm attempting to find the length of a NURBS curve, but I'm not having any luck (I'm also not entirely sure if NURBS are more of a programming thing, I initially asked this question over on Stack ...
1answer
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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 ...
2answers
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### Formula to display a $3D$ $90$ degree pipe bend

I am trying to display a $3D$ Pipe with $90°$ bend. I am writing code for it, but I am sure this is more of a mathematical question as a programming one. It would be nice if anyone could help me ...
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### To find the center of gravity of a homogeneous tetrahedron

The center of gravity coordinates of a triangle can be calculated $O(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3},\frac{z_1+z_2+z_3}{3})$ where $P_1,P_2, P_3$ are the corner points of a homogeneous ...
0answers
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### Rotating a cube about an axis through opposite vertices

I have a cube made using CSS transforms that I'm trying to animate rotating about an axis going through 2 opposite vertices. What I have: Initial cube: ...
1answer
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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 ...
1answer
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### Why does a 3d line of segments with constant angles always make a helix?

I have a chain of discrete segments, of equal sizes, built by the following rules: 1)every next segment rotates around it's Y axis by 7 degrees, 2)then it pivots at the join with the previous ...
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### Multiplication with vectors.

Well, I'm not quite sure if I chose right terms for my problem but I will give it a chance. Here, I have some tasks and examples ( http://www.mif.vu.lt/matinf/asm/gr/p12.pdf ). On the bottom of the ...
2answers
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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 $c$ ...
2answers
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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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### What is the difference between $z=0$ plane and $26z=0$ plane

I'm using this site to calculate a plane equation. The points are $(2,3,0)$, $(5,1,0)$ and $(6,9,0)$. The result is $26z = 0$ plane. Is there a difference between $26z =0$ and $z = 0$? Moreover, ...
0answers
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### Intersection volume of two oriented bounding boxes

I have been searching the web for a while now, but to my surprise I haven't found a algorithm to the following problem yet: Given are two oriented bounding boxes, that is, they generally are not axis ...
2answers
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### How to rotate a plane in 3-D using standard form?

I have a set of points $N = \{n_1, n_2, ...\}$ on a plane $z = 0$. And I have another set of points $M = \{m_1, m_2, ...\}$ on plane $ax + by + cz + d = 0$. $|N| = |M|$ $\forall n_i, n_j \in N$ and ...
1answer
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### Finding the missing coordinate of a point within a 3D triangle

We have an equilateral triangle $ABC$ in 3-dimensional space. The points are known, such as: $A = (x_1,y_1,z_1)$ $B = (x_2,y_2,z_2)$ $C = (x_3,y_3,z_3)$ Point $P$ is on triangle $ABC$. If I know ...
2answers
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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 ...
1answer
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### Rays in the space

I have a nice problem from a mathematical circle: Let n be a positive integer. Determine the smallest n with the property in the space having
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### Converting 3D into 2D

I have a quad and I'm trying to convert its vertices so that they're facing the camera which is lying at 0,0,1 looking down the Z, or not even specifically facing the camera, just so they're facing up ...