The (3d) tag is for things related to 3-dimensions. For geometry of 3-dimensional solids, please use instead (solid-geometry). For geometry that is not on a plane, but otherwise agnostic of dimensions, perhaps (euclidean-geometry) or (analytic-geometry) should also be considered.

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Volume of a tetrahedron given length of edges.

I found this method to find the volume of a tetrahedron given the length of edges on Wikipedia I found this Interesting, and was looking for a formal proof, but didn't find it anywhere. Could ...
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1answer
39 views

Test if a point is inside a 3D cuboid

I have a cuboid in 3D space, it is not regular at all. I do have the coordinates of its 8 vertices and my problem is how to determine a given point coordinate is inside or outside this cuboid. I ...
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25 views

Isometries of S^3 and some Lie algebras

By considering $S^3$ as the group of unit quaternions, and letting it act on itself from both the left and right, one can get an isomorphism $SO(4)\cong (S^3\times S^3)/C_2$, where the $C_2$ subgroup ...
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1answer
36 views

When are two 3D Lines parallel in Plücker matrix form?

When are two lines in 3 dimensional space parallel, when the lines are both represented by Plücker matrices $L$ and $L'$. I'm trying to prove the solution to this question: ...
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1answer
52 views

Torus helix radius change equation

If we draw a closed helix trajectory on the surface of a torus (with helix center axis corresponding to that of torus), the radius will cyclically change between inner and outer radius (r and R). Can ...
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1answer
17 views

Number of variables and dimension of a function

Why is a function $f(x)$ called a single-variable function if it has coordinates represented by $x$ and $y$? Can it be called a 1D function if its plot is 2D? Subsequently, can two-variable functions ...
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0answers
21 views

Intersection of a Plane with the Riemann Sphere

While reading Fundamentals of Complex Analysis by Saff and Snider, I came across an example (see page 47, edition 3) where it is shown that "all lines and circles in the $z$-plane correspond under ...
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1answer
21 views

Why 2 equations of the form F(x,y,z) = 0 for one 3D curve

It says in my analysis 2 book that a curve is given by $F_1(x,y,z) = 0$ and $F_2(x,y,z) = 0$. Why do we need two equations of $x,y,z$ To define a curve in 3D, shouldn't one be enough?
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2answers
77 views

The easiest way to find distance between point and a line defined by two points in 3D [closed]

Let's assume I have two points with coordinates $(x,y,z)$ and $(x_1,y_1,z_1)$ and there is line between them. I am given a point with coordinates $(x_2,y_2,z_2)$. What's the easiest way to calculate ...
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1answer
29 views

Rotating a plane defined by a normal and a distance from the origin around an arbitrary point in 3D space

I have a plane defined by its normal and its distance from the origin. I have a rotation matrix and a point in 3D space around which to do the rotation. What formula will allow me to do the rotation? ...
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2answers
38 views

Considering a convex polygon lying on a plane in 3D space, how can I know if a point on that plane lies inside or outside that polygon?

I have a plane in space and a polygon in it. I know the position of each vertices making the polygon. I also know the position of the point on the plane. How can I know whether the point is inside or ...
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3answers
756 views

Center of Mass in 3D object?

How would I find the center of mass in a 3D object (a "spinning top" or "dreidel") that consists of a cylinder welded on top of a box welded on top of an upside down cone? Assume building material is ...
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2answers
18 views

Make a multivariable function continuous

What can we do with this function, so the function will be continuous in $(0,0)$? $f:\mathbb{R}^2\rightarrow\mathbb{R}:(x,y) \mapsto \frac{x^2+y^2-x^3y^3}{x^2+y^2}$ What I think we should do, is: ...
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3answers
79 views

Showing that a Unit Speed Curve is a Circle.

In my recent differential geometry tutorial, we were given the question: Given the unit speed curve, $$\boldsymbol{r}(s)=\left(\frac{4}{5}\cos(s),1-\sin(s),-\frac{3}{5}\cos(s)\right)$$ show that ...
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0answers
92 views

Equation for Circle in 3D Space Given Center, Radius, and Point

I'm looking for how to derive the equation of a circle, in 3D space, given the following information: The Center Point The Radius One point on the circle I understand that this is functionally the ...
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2answers
90 views

3D Geometry Problem

If we have 4 equal sized spheres with radius $R$ arranged surrounding another smaller sphere such as to make a triangular pyramid from the centers of the $4$ spheres with radius $R$. The radius of ...
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1answer
36 views

Algorithm for solving line line intersection in 3d

I am trying to find an algorithm that a computer can execute that finds the intersection point between two lines each defined by a point on the line and a direction vector. Does anyone know of one? It ...
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0answers
14 views

For an app teaching about polyhedra, what are some core characteristics to include?

For fun: I'm building a 3d app that teaches about polyhedra. What should I include? The obvious didactic elements for each polyhedron would be: Fundamental polygon's Vertices 
Edges
 Faces
 (and ...
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1answer
73 views

Drawing 3D stomach structure in Matlab [closed]

I would like to plot a 3D structure representing the stomach in Matlab. A sketch of what it should look like is here: http://thoracicsurgery.stanford.edu/patient_care/images/normal-stomach.jpg Still, ...
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1answer
73 views

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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1answer
36 views

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 ...
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2answers
50 views

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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1answer
30 views

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 ...
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30 views

Get Vector From Angle In $3D$ Space

I have a camera angle in $x,y,z$ with values between $0$ and $360$, I'm trying to compute this into an 'aim vector' which would have values between $0,0,0$ and $1,1,1$ depending on what the angles ...
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1answer
22 views

Dot product of any point on plane and its normal

I was trying to find the distance between a point and a 3D line with parametric equations. On the web, I found a video detailling the steps. https://www.youtube.com/watch?v=9wznbg_aKOo At 2:20, the ...
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0answers
16 views

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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0answers
54 views

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 ...
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0answers
42 views

Rotation plane on the sphere (quarternion)

I asked similar question on stackoverflow but still no answers.http://stackoverflow.com/questions/25185329/image-rotation-with-the-gyro-data-math I assume it is more math than programming problem. ...
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2answers
51 views

Two and Three Variable Limit Questions

Find the following limits, if they exist. $$\lim_{x,y\rightarrow 0,0}\frac{x^2 + \sin^2 y}{\sqrt{x^2+y^2}}$$ I believe we're suppose to use the squeeze theorem on this first one above. Possibly ...
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1answer
53 views

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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0answers
38 views

slope of a plane

I'm trying to understand the math behind 3d perspective clipping algorithm dixit: We need four constant to express the equations of the four side planes. These are the slopes of the planes in ...
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2answers
87 views

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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1answer
57 views

Find out whether two rectangles are intersecting in 3D space

I've got two rectangles in 3D space, each given by the coordinates of their 4 corners. They are not axis aligned, meaning their edges are not necessarily parallel/perpendicular to the world axes. Each ...
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2answers
41 views

Efficiency in vector translation by matrix instead of vector

I try to understand math for 3D games. If I want to translate a point, I may do it in two ways: 1. Using vector summation. 2. Using matrix multiplication. For example: Initial vector $p =(1,2,3)$. ...
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1answer
31 views

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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2answers
61 views

Derive a quaternion from three axis

My problem originates from some code that I'm writing to parse an obscure file-type in which a geometric entity is defined in it's own 'local space', and a rotation and translation are provided to ...
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1answer
86 views

Making a function periodic

This might not be the best place to ask this question, but here it goes... I'm creating a game and need 3D sea waves. Since it's for mobiles, there's no time to generate entire screen worth of waves ...
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0answers
64 views

Water swallowing in Matlab

I want to simulate some water passing through a vertical cylinder in Matlab, and I would like to implement a 3d animation of it. I built the cylinder using the patch function, but I do not know how to ...
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2answers
167 views

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 ...
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1answer
42 views

Elevation of 3D function

$f(x,y) = \begin{cases} x^2/y & y \neq 0 \\ 0 & y = 0\end{cases}$ I need to draw the elevation (or you may call it Equivalent curve) of this function and I don't know how to draw them. Can ...
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0answers
119 views

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: ...
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1answer
32 views

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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1answer
31 views

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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1answer
87 views

Software to easily draw 3d plots from functions

my problem is that I need a way to quickly check results of my, that is to say, homework. I think that the best way to do this is to draw a plot of a function to quickly see whether my solution is ...
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2answers
93 views

Area of projection of cube in $\mathbb{Z}^3$ onto a hyperplane

A cube with vertices $(\pm 1, \pm 1, \pm 1)$ gets projected into the plane perpendicular to vector $\mathbf{n}\in S^2$. The projection is a hexagon, how do I find the area? I think I can just ...
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1answer
72 views

To find the volume of the region that is bordered by 4 points in 3D space

To find the volume of the region that in the points $A(x_1,y_1,z_1),B(x_2,y_2,z_2),C(x_3,y_3,z_3),D(x_0,y_0,z_0)$. Let's define a 4X4 matrix to determine plane equation that are on $A,B,C$ ...
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2answers
298 views

Parametric equation for intersection of curve

Here's the three part question: A) Find parametric equations for curve which is the intersection of the cylinder $x^2 + z^2 = 1$ and the plane y = -x. B) Show that the curve lies on the surface $x^2 ...
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1answer
78 views

Probability that two circles in space are linked

Let $C_0$ be a circle centered on the origin, and $C_1$ a circle centered on $(1,0,0)$, center distance of $1$. Q1. If both $C_0$ and $C_1$ are randomly oriented and have the same radius $r ...