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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2
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1answer
130 views

Algorithm for finding orientation of each face on a polyhedron?

I am working on making a dice rolling application and I need to find out how far in each of the three dimensions I must rotate each of the dice to make the correct side face the camera so the user can ...
1
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0answers
76 views

3d Implicit Trigonometry help?

I'm trying to understand implicit 3D trigonometry, specifically with this equation: $$\sin(y)+\cos(z)=\cos(x)$$ Can someone please explain to me what is going on with this equation? I really can't ...
0
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1answer
113 views

What will happen if I try to print an impossible solid into a 3D printer? [closed]

What would be the result of a 3D modeled impossible solid, like the Penrose Triangle, printed out of a 3D printer?
0
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2answers
1k views

hyperbola curve formula in 3 dimensions

Cartesian formula for 2d hyperbola curve is $x^2/a^2-y^2/b^2 = 1$. What is the formula for a 3d hyperbola curve?
0
votes
2answers
133 views

Rotation matrix - rotate a ball around a rotating box

I've a 3D box: center point = (a,b,c), width = w, height = h, ...
1
vote
3answers
462 views

What is the formula for a 3D line?

Just like we have the formula $y=mx+b$ for $\mathbb{R}^{2}$, what would be a formula for $\mathbb{R}^{3}$? Thanks.
2
votes
2answers
107 views

Books for Geometry processing

Please suggest some basic books on geometry processing. I want to learn this subject for learning algorithms in 3d mesh generation and graphics. Please suggest me subjects or areas of mathematics i ...
1
vote
1answer
311 views

3D Circle/ground intersection

This one stumps me: A circle in 3D space given by its center = $(0.15, 0.5, 1.0)$, its radius $=64$ and an orientation vector that points away from the circle's plane $(0.251, -0.796, 0.551)$ How ...
4
votes
2answers
173 views

Rotation of a point in 3d space

I'm trying to rotate a point around a single axis of a 3D system. Given $P=\begin{pmatrix} 101 \\ 102 \\ 103 \end{pmatrix} $, And the rotation matrix formula for rotation around the X axis only, I ...
2
votes
2answers
169 views

Is the value of $\pi$ in 2d the same in 3d? [closed]

I am starting with my question with the note "Assume no math skills". Given that, all down votes are welcomed. (At the expense of better understanding of course!) Given my first question: What is ...
2
votes
1answer
90 views

question from hatcher basic 3 manifolds

The question is: why should a homologically trivial embedded sphere in a simply connected (not necessarily compact) 3 manifold M bound a compact 3 manifold embedded in M? I had this problem reading ...
0
votes
1answer
471 views

Intersection between sphere and cylinder

I have a sphere and a cylinder. I have the center and the radius of each of them. the sphere: radius = $r_1$ center = $(x_1,y_1,z_1)$ the cylinder: radius = $r_2$ height = $h_2$ center = ...
7
votes
2answers
557 views

Cross section is a regular hexagon.Is it a cube?

One of the cross sections in a rectangular box is a regular hexagon.Prove that the box is a cube I tried to prove that certain lengths were equal by showing that certain triangles are congruent but ...
0
votes
1answer
596 views

Rotate a plane along a line in 3d space

I have a plane A in 3D which can be defined either by the scalar plane equation or by its normal n. I want to find a new plane B which is orthogonal to plane A but shares an edge with plane A. I.e. I ...
0
votes
2answers
554 views

Calculate distance from plane to parallel plane in O using vector and normal

I'm trying to figure out what's the best method to get the distance between two planes where i have the normalized vector of the plane and a point in the plane. What I want to do is to create a ...
0
votes
1answer
370 views

Shortest distance between a 3D parametric surface and a point

Right now I'm working on a library for finding the distances between objects in Lua. I've had some trouble finding the distance between a point and a bounded plane. I'm using these parametric ...
2
votes
3answers
975 views

Composition of two axis-angle rotations

Please note that I am not referring to Euler angles of the form (α,β,γ). I am referring to the axis-angle representation, in which a unit vector indicates the direction axis of a rotation and a scalar ...
5
votes
4answers
2k views

What's the best 3D angular co-ordinate system for working with smartphone apps

This is very much an applied maths question. I'm having trouble with Euler angles in the context of smartphone apps. I've been working with Android, but I would guess that the same problem arises ...
0
votes
1answer
795 views

Finding point in two parallel lines in 3d?

The line $L_1$ that goes through the point $A(4,3,-2)$ and its parallel to the line $(x=1+3t, y=2-4t, z= 3-t)$, if $P(m,n,-5)$ belongs to $L_1$, determine the values for $m$ and $n$ I really don't ...
2
votes
1answer
103 views

Rotate 3d plane

I have a plane in 3D space that formed from 3 poin $P_1=(x_1, y_1, z_1)$, $P_2=(x_2, y_2, z_2)$, $P_3=(x_3, y_3, z_3)$ I want to rotate and transform this points (equally related plane) into 2D space ...
3
votes
1answer
282 views

Finding intersection of 2 planes without cartesian equations?

The planes $\pi_1$ and $\pi_2$ have vector equations: $$\pi_1: r=\lambda_1(i+j-k)+\mu_1(2i-j+k)$$ $$\pi_2: r=\lambda_2(i+2j+k)+\mu_2(3i+j-k)$$ $i.$ The line $l$ passes through the point with ...
1
vote
1answer
634 views

Coordinate Transformation on Local coordinate system

I am having a point $P(x,y,z)$ in $3D$ with respect to global coordinate system. I want to create an another Local Coordinate System by picking three points $N1, N2, N3$ in 3D. Now I want to know the ...
1
vote
1answer
519 views

Finding the possible lengths and widths, given a surface area.

Short Version of Question: Each of $l$, $w$ and $k$ is a positive integer. Determine all possible values for $l$ and $w$ such that $l \ge w$, and $(k + 1)(l + w - 2k) = 133$. Long Version of ...
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vote
0answers
97 views

Vector Tangent to Curve of Intersection

I am having problems solving this. Find a vector tangent to the curve of intersection of $z = 4x^2 + y^2$ and $z=(27-x^2-y^2)^{1/2}$ at the point $(1,1,5)$. I'm able to do this kind of thing using ...
0
votes
1answer
41 views

Plotting a function $\phi: C \to R$ in $R^3$ by writing it in terms of $\phi: R \times R \to R$.

I have a complex polynomial $f(z)$ and I would like to plot a 3D graph that takes in $x$ and $y$ (as the real/imaginary parts) and outputs the modulus of the result. How can I write, for example ...
2
votes
0answers
134 views

Big data: 3D clustering with over 40 groups

I am a computational neuroscientist and I struggling over a problem; I have around one hundred 3D matrices (I am working on MATLAB at the moment), each of them is 121x145x121. Any 'cell' stores a ...
2
votes
1answer
356 views

Is this the right equation for this 3D surface?

Is $\frac{\sin \sqrt{x^2+y^2+z^2}}{\sqrt{x^2+y^2+z^2}}$ the right equation for this surface? I am confused what $z$ is doing in there (unless this is an implicit equation). I get something fairly ...
0
votes
1answer
76 views

Commutative applying rotations around three axis

Rotating an object in a 3 dimensional space by euler angles might be intuitive but comes with some problems. First, the order of applied rotations around the different axis matters. Second, there is ...
5
votes
0answers
294 views

How can I solve the Poisson PDE efficiently and fast in cylindrical coordinates?

I am trying to numerically solve the Possion PDE in cylindrical coordinate system. $$\Delta f = {1 \over \rho} {\partial \over \partial \rho} \left(\rho {\partial f \over \partial \rho} \right) + {1 ...
0
votes
0answers
37 views

How to derive an average Z value among arbitrarily distributed X, Y, Z points

I am triangulating using Delauney algorithm to create a 2D (x, y) flat surface in OpenGL. There are "control points" available, with (x,y,z) values that I need to apply to the triangulated surface to ...
3
votes
1answer
80 views

Finding a point in an ellipsoid

I know the semi-principal axes $(x,y,z)$ of the ellipsoid $E$ (centered at the origin). Given the normalized direction vector $\vec{v}=(a,b,c)$ pointing from the origin to the surface, how can I find ...
10
votes
0answers
295 views

Visualizing a Calabi Yau

I would like to understand how I can visualize the quintic threefold $$ z_1^5 + z_2^5 + z_3^5 + z_4^5 +z_5^5 - 5\psi z_1z_2z_3z_4z_5 = 0$$ For a similar problem, Hanson proposes the following: ...
1
vote
3answers
2k views

Nullify (zero out, cancel) rotation in an arbitrary axis in a Quaternion

Question: How do you nullify (zero out) rotation around an arbitrary axis in a Quaternion? Example: Let's say you have an object with quaternion orientation $A$. You also have a rotation quaternion ...
2
votes
2answers
147 views

How to get angle bewteen two vectors in range -1 to 1 without using arc cosine?

Given two normalized vectors in 3d space, how can I get a value from $-1$ to $1$ based on their angle without using arc cosine? With use of arc cosine, I think this would give me the correct result. ...
3
votes
0answers
73 views

How to solve a distance problem inside of a picture?

sorry for my bad english. I have the following problem: In the picture you can see 4 different positions. Every position is known to me (longitude, latitude with screen-x and screen-y). Now i want ...
2
votes
1answer
70 views

Disable one angle of rotation

I'd like to disable one angle of rotation of an object rotating in 3D space. Imagine a camera rotating around and displaying objects as they are in space. I'd like this object to be fixed on the ...
1
vote
4answers
94 views

Find the equation of plane containing line described by

Please help me in this really easy task Find the equation of plane containing line described by $x+3y-2z=1$, $2x-y+2z=3$, containing point $(1,1,3)$
1
vote
0answers
61 views

Are there 3D tilings of a 3D projective hyperplane or 3-sphere?

I noticed that pentagons tile the projective plane (a spherical dodecahedron). Something they do not do on a flat euclidean plane. Is there analogous 3D tilings (honeycombs) of a 3D projective ...
1
vote
1answer
42 views

What does delta_length mean in this context?

and thanks for looking at this question! I'm trying to extend a force directed graph layout to not just lay out a graph in 3d (which the following implementation does a fine job of) but to also do so ...
2
votes
1answer
316 views

A controlled trapezoid transformation with perspective projecton

I'm trying to implement a controlled trapezoid transformation in Adobe Flash's ActionScript using the built-in perspective projection facility. To give you an idea of how the effect looks like: ...
2
votes
4answers
142 views

Why can a plane be defined with its normal line?

The title is worded a bit confusingly. I apologize, I just couldn't think of how to phrase it. Either way, say you have the plane $x+2y-4z=8$ The normal line will have direction $x=1, y=2, z=-4$ So ...
1
vote
1answer
105 views

How to combine bezier curves to a surface?

My aim is to smooth the terrain in a video game. Therefore I contrived an algorithm that makes use of bezier curves of different orders. But this algorithm is defined in a two dimensional space for ...
1
vote
1answer
3k views

About vector form of a line passing through 2 points.

According to my book: Equation of line passing through 2 points with position vectors $a$ and $b$ is $$r = a + K(b - a)$$ My question: If we are given 2 points how do we determine which point is ...
1
vote
1answer
4k views

Moving point along the vector [closed]

I'm making a game. I have came across a problem. I have to move a point along a vector for some distance. Can anyone help me? Any ideas?
2
votes
1answer
233 views

Use pythagoras in a cuboid to find x.

my daughter has a question and I am lost how to solve it. I have a rectangular box with the following dimensions (see below picture) Height: $2x-1$ Width: $x+8$ Length: $2x+4$ the line running ...
0
votes
0answers
222 views

Rotating a system of points to obtain a point in a given place

Given an arbitrary number of points which lie on the surface of a unit sphere, one of which is arbitrarily <0, 0, 1> (which I will call K) in a rotated system ...
3
votes
1answer
337 views

Draw an arc in 3d coordinate system

I have some legacy code which is supposed to draw an arc with constant radius in 3d space however it is drawing the arc in the wrong position. I would like to know and understand the mathematical ...
0
votes
3answers
131 views

How to calculate triangle-line collision in 3D?

If there is a given triangle (tx1, ty1, tz1), (tx2, ty2, tz2), (tx3, ty3, tz3) and two given point of a line ...
3
votes
3answers
495 views

Tetrahedron problem (proving)

Prove that if $P$ is the intersection of the altitudes of a tetrahedron $ABCD$ and $r$ is the circumradius then $PA^2+PB^2+PC^2+PD^2=4\cdot r^2$.
0
votes
0answers
72 views

Turn any shape to circle

I'm looking at trying to calculate and re position 3d vectors to align in a new position to form a circle. I've achieved this already however only when all points are evenly distributed in the same ...