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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3
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7answers
887 views

Software to display 3D surfaces

What are some examples of software or online services that can display surfaces that are defined implicitly (for example, the sphere $x^2 + y^2 + z^2 = 1$)? Please add an example of usage (if not ...
1
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4answers
126 views

Best program for 3D plotting

I've hit a roadblock with pgfplots where it has difficulty plotting multiple functions at the same time in 3D. As it states in the manual on page 114, "it cannot combine different \addplot commands, ...
0
votes
1answer
50 views

Intersection of Three Planes proof

I'm supposed to be making a study guide answer for this question, but I'm struggling with proof. Show that the three planes intersect at the point provided that Note that the ...
0
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2answers
29 views

Width of rotated plane

I'm trying to get the width of a rotated plane, but my knowledge of trig functions didn't really help me get what I want. I have a plane, that is $310$ units wide, and is $200$ units away from the ...
0
votes
2answers
32 views

Final transformation matrix

I have a 3d object, to which I sequentially apply 3 4x4 transformation matrices, $A$, $B$, and $C$. To generalize, each transformation matrix is determined by the multiplication of a rotation matrix ...
0
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1answer
27 views

3 Points in 3D Space to Develop an Arc or Circle

Background: I'm a Robotics Engineer and I am trying to develop a more flexible, modular, and robust program for our welding robots, which will minimize teaching time for new robots and also minimize ...
2
votes
1answer
520 views

Jacobian of exponential mapping in SO3/SE3

Following this post Jacobian matrix of the Rodrigues' formula (exponential map) What if I really need the Jacobian of the exponential mapping function in $\omega \neq 0$? Basically, I want to ...
2
votes
3answers
59 views

possible polyhedra from euler's formula

I'm not very clear with the euler's formula, and I couldn't find it anywhere. I'm sorry if it is a double post. F + V - E = 2 Is the euler's formula. If the equation balances, is it polyhedra all ...
0
votes
4answers
48 views

Points on 3d line

Say we have $2$ points on a 3d line, point $A(x,y,z)$ and point $B(x,y,z)$. If we want to get the coordinates of a third point, beyond point $B$ but a certain distance from point $A$, how would we do ...
1
vote
1answer
505 views

What is an isosurface?

I am trying to understand the marching cubes algorithm. I would like very much an easier definition of an isosurface than what is available online. Could anyone please explain it? Thanks.
0
votes
4answers
40 views

How to find perpendicular vectors in 3D

Find all values of a such that the vector $q = \langle 2, a, –2\rangle$ is perpendicular to the vector $p = \langle –3, a, 5 \rangle$.
4
votes
1answer
55 views

8 cubes ($2$x$2$x$2$) crossed by a straight line

There are 8 cubes forming a bigger cube whose dimension is $2$ x $2$ x $2$. Let a straight line (or a laser) try to pierce through as many small cubes as possible. At most how many small cubes can be ...
2
votes
2answers
173 views

Calculate the viewing-angle on a square (3d-calc)

I'm in big trouble: My program (Java) successfully recognised a square drawn on a paper (by its 4 edges). Now I need to calculate, under which angle the webcam is facing this square. So I get the 4 ...
0
votes
0answers
19 views

Intersection of two moving objects in 3D

There are two objects, where the known data is the position and velocity in 3D vector format. I`m interested in the time and position of the intersection between the two, and possibly without ...
1
vote
2answers
376 views

puzzle 3-d visualization

729 small cube are painted pink on each face and then arranged to form 27 identical middle-size cubes.Each middle size cube is painted black and then arranged together to form one large cube. And ...
-1
votes
0answers
15 views

3D Geometry-If alpha /2 ,beta /2 and gamma /2 are the angles with 3 axes.Then, cos alpha + cos beta + cos gamma [on hold]

If alpha /2 ,beta /2 and gamma /2 are the angles which a line makes with the x,y,z axes respectively.Then, cos alpha + cos beta + cos gamma = ? a-> 1 b-> (-1) c-> 2 d-> 3
0
votes
1answer
41 views

Perpendicular vectors in $\Bbb R^3$

Hi I am struggling with this simple question. Let $\vec{v}$ be a unit vector in $\Bbb R^3$. How can I construct two periodic functions $\vec{x}(\theta)$ $\vec{y}(\theta)$ such that $\vec{v}$, ...
0
votes
1answer
20 views

Change from one cartesian co-ordinate system to another by translation and rotation.

There are two reasons for me to ask this question: I want to know if my understanding on this issue is correct. To clarify a doubt I have. I want to change the co-ordinate system of a set of ...
4
votes
3answers
65 views

Sphere packing question

I'm a secondary school maths teacher, currently on my holidays working through some maths problems for fun. Here is one I have done, but it felt too easy, so if you could check if there's any ...
7
votes
1answer
453 views

Is a 3D Mandelbrot-esque fractal analogue possible?

I understand that (unlike complex numbers) there's no consistent 3 dimensional number system (even 4D loses some nice properties). Regardless, I'm wondering if there might be a 'trick' to create a 3D ...
2
votes
3answers
4k views

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 ...
3
votes
1answer
511 views

3D Rotation Decomposition?

I have a 3D local xyz coordinate system placed in a world ENU (East-North-Up) coordinate system. The current relationship ...
0
votes
3answers
46 views

Do these points make a straight line?

I'm trying to prepare for my calculus 3 class coming up this fall and doing some practice problems. I'm having a hard time visualizing some of these 3D coordinates. $D(0,-5,5)$ $E(1,-2,4)$ ...
1
vote
1answer
360 views

Ellipsoid intersection

Let $E$ be an ellipsoid centered at $p = (x,y,z) \in \mathbb{R}^3$ and let $T:\mathbb{R}^3 \to \mathbb{R}^3 $ be a linear transformation which transforms $E$ to a unit sphere. Let $R$ be the ray $p_0 ...
0
votes
2answers
35 views

Find closest point on a plane to a given point. Discrepancy with normal vector.

I have a point $(9,5,0)$ and a triangle with points $(1,1,0), (3,3,1), (6,1,0)$, let's label them as $A,B,C$ respectively. In order to get the normal vector, I do the cross product of two vectors. If ...
3
votes
1answer
65 views

Find the shortest distance from the triangle with with vertices in $(1,1,0),(3,3,1),(6,1,0)$ to the point $(9,5,0)$.

I have to find the shortest distance from the triangle with with vertices in $(1,1,0),(3,3,1),(6,1,0)$ to the point $(9,5,0)$. I cannot figure out how to do this. There are three possible cases: ...
1
vote
0answers
24 views

Given a single point in 3d space, and 3 points that make up a triangle, find the closest point in/on the triangle to the point.

Given point $(p,q,r)$ and 3 points which make up a triangle, find the closest point in the triangle to the point in space. From the triangle, we can find the equation of the plane $Ax+By+Cz+d=0.$ ...
0
votes
1answer
305 views

How can I transform a 3D triangle to xy plane

Suppose I am given a triangle ABC and its corresponding vertex coordinates in 3D. I want to transform ABC in such a way so that vertex A lies on global (0,0,0) coordinate, B lies on (dist, 0, 0) ...
1
vote
1answer
32 views

Small Stellated Dodecahedron, generating triangle vertices

I have been trying to draw a small stellated dodecahedron (would post an image if I had enough rep) using OpenGL, and would like to generate the vertices programmatically. I'm looking for a way to map ...
0
votes
1answer
405 views

Calculating normals for a polygon mesh (3D computer graphics)

I want to write a program to generate arches, a common architectural form, and export them to a wavefront object format for sharing with various three dimensional graphics editors. To do this, I need ...
1
vote
1answer
21 views

Can I break up the 3D line integral $\int_{K,p} (2xydx + (x^3 + 3z)dy + 3ydz)$ in three single integrals?

$$\int_{γ,p} (2x \ y \ dx + (x^3 + 3z) \ dy + 3y \ dz)$$ where $$γ = [(0, 0, 0),(0, 1, 3)] ∪ \{ (x, y, z) ∈ \mathbb{R^3}|y = 0, \ x^2 + (z − 3)^2 = 9, \ x ≤ 0\} ∪ [(0, 0, 6),(1, 1, 6)]$$ and p is the ...
3
votes
5answers
279 views

Is the rhombic dodecahedron the only isohedral polyhedron that tiles 3-space (other than the cube)?

Is the rhombic dodecahedron the only face-transitive (or isohedral, i.e. all faces are the same) polyhedron that seamlessly tiles 3-dimensional Euclidean space (other than the cube)? I'm looking ...
3
votes
4answers
377 views

3D coordinates of circle center given three point on the circle.

Given the three coordinates $(x_1, y_1, z_1)$, $(x_2, y_2, z_2)$, $(x_3, y_3, z_3)$ defining a circle in 3D space, how to find the coordinates of the center of the circle $(x_0, y_0, z_0)$?
4
votes
2answers
125 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 ...
1
vote
0answers
517 views

Helix around helix parametric equation?

I know the parametric equation for a $3D$ helix is: $x = R \cos t$ $y = R \sin t$ $z = h t$ Can somebody explain to me this parametric equation (image and equation from Wolfram) for a "Helix ...
2
votes
0answers
53 views

3D Shape with only coplanar faces?

I just thought of this problem, and it's bugging me that I can't find any sort of shape that fits it. Are there any 3D shapes with only faces that have coplanar matches with other faces in the shape? ...
2
votes
2answers
45 views

How to rotate cuboid to plane

I have a cuboid with 8 points that is axis aligned with its center at the origin 0,0,0. Now I have a plane and want my cuboid to rotate so that instead of being axis aligned, it is now aligned to this ...
1
vote
1answer
33 views

How to find the points of intersection of the perpendicular vector two skew lines

Correct me if im wrong, but this is what i know so far The cross product of two skew lines is the perpendicular vector between both those lines. The perpendicular vector intersecting two skew lines ...
2
votes
0answers
63 views

Math behind No Man's Sky, or Math of Minecraft in Space [closed]

I recently received a question from one of my students which is a bit outside my life experience. However, I expect this may be of interest to many: I was reading up on a new video game that's ...
0
votes
0answers
28 views

Calculus | Parametrization of boundary in $\mathbb{R^3}$

The Problem Given the volume $$ K = \left\{ (x,y,z)\in \mathbb{R^3} \big| \frac{x^2}{9} +y^2 \le z^2 +1, -\frac{1}{3}\sqrt{\frac{x^2}{9} +y^2} \le z \le 3 \right\} $$ What are $a$, $b$, and $K(z)$ ...
1
vote
1answer
20 views

In an icosahedron subdivided n times, how can I find the coordinates of adjacent centroids?

I think it would be helpful to refer to this image when trying to follow my description: http://i.imgur.com/nRXQo3W.jpg (taken from http://experilous.com/1/blog/post/procedural-planet-generation). ...
0
votes
1answer
36 views

Normal to a 3 Dimensional line

So I have a 3D line: $(0, 0, 0)+t(3, 4, 7)$ and I'm trying to find the normal of this. I know the gradient of the normal would normally be $\frac{-1}{\text{gradient}}$ but I'm not sure how you would ...
2
votes
3answers
59 views

rotations in 3d space

When looking at rotations in 3d space, does specifying two points (say point A is rotated to point B) determine the whole rotation, or is there a degree of freedom left?
0
votes
1answer
282 views

Direction Cosines and Rotation Angles

I'm rotating an object in $3D$ space with respect to a relative base, or reference frame. I'm using a normal vector to represent the rotation angles. Suppose you have an object parallel to the ...
2
votes
0answers
21 views

can't figure out multilateration with xyz positions of each post and difference in time

I'm having some real issues figuring out multilateration. I'll start by saying I'm not a math whiz, but I am usually able to figure most things out, but this one has been throwing me through a loop ...
2
votes
0answers
11 views

How can i reflect position and direction vectors from a plane

I'm now working on a project that has mirrors. I'd like to reflect a virtual camera and the way which i can do this is to reflect two vectors - position and normalized direction vectors of the camera. ...
1
vote
1answer
20 views

Fracturing of a 3D Object

Although this is a computer science applied subject, all the underlying logic is mathematical and geometric. I am trying to write code that will enable me to split an object into random fragments, ...
2
votes
2answers
337 views

Equation of a parabola in 3D space

I have two points with coordinates A(x1,y1,z1) and B(x2,y2,z2). There is a third point which is vertex(lowest point) of the parabola. I only know z-coordinate of this point. I need to find coordinates ...
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vote
2answers
18 views

How to find the 3d direction of a particle sliding down an inclined plane?

So, I'm working in 3D space. I have a frictionless particle sitting on an inclined plane. There's gravity (pushing down on the Y axis), so the particle will slide down the slope. If I know the ...
0
votes
2answers
58 views

How to derive the 3D equation of a torus?

I'm doing a presentation on 3D surfaces for college and one of the equations I am using is a Torus. I know that the equation is $$z^2 = 25 - \left(10 - \sqrt{x^2 + y^2}\right)^2$$ For a torus with ...