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
33 views

What is the equation of a 3D cone with generalised tilt?

What is the equation of a 3D cone with generalized tilt? I've noticed that in most equations given to represent a cone, there is no parameter which defines the tilt of the cone in 3D space and that ...
3
votes
2answers
105 views

How do I calculate this loop spline given the length, angle and horizontal offset?

I'm developing a formula to calculate a loop spline from a length, angle and horizontal offset. I can successfully calculate the loop from the first two parameters, but taking the horizontal offset ...
2
votes
3answers
9k views

How to find line parallel to direction vector and passing through a specific point?

I am give the point $(1,0,-3)$ and the vector $2i-4j+5k$ Find the equation of the line parallel to vector and passing through point $(1,0,-3)$ Could one use the fact that the dot product between the ...
0
votes
2answers
31 views

Quaternion Rotation

I am modelling rotations of a rectangular box (3 dimensions) in Matlab using Quaternion theory. Using the theory found on https://en.wikipedia.org/wiki/Quaternions_and_spatial_rotation I have ...
0
votes
1answer
95 views

Text book on solid geometry/stereometry, without involving analytic geometry

As the title says I'm searching for a textbook, about solid geometry, without involving analytic geometry. The material which the book should cover is the stereometry learned in the eastern bloc. An ...
3
votes
1answer
5k views

How to find perpendicular distance from point to plane in $3D$.

The line $L_1$ passes through point $A$ whose position vector is $3i - 5j + 4k$, and is parallel to the vector $3i + 4j + 2k$. The line $L_2$ passes through the point $B$ whose position vector is $2i +...
0
votes
1answer
91 views

Trigonometric Word Problem in 3D

The question I am having trouble on is as follows: "As an Expert Mathematics Witness, you have been presented with a Ballistics Report, and a Police Report as your evidence. Use the information ...
0
votes
1answer
647 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 ...
0
votes
1answer
17 views

What is the equation for the number of combinations of 4 cubes that can be rotated on all axes

I have been trying to work out the number of possible unique combinations of 4 cubes where they can be rotated on any axis. So for example if all the faces of all the cubes where unique across the ...
5
votes
6answers
7k views

Rotating one 3d-vector to another

I have written an algorithm for solving the following problem: Given two 3d-vectors, say: $a,b$, find rotation of $a$ so that its orientation matches $b$. However, I am not sure if the following ...
4
votes
1answer
1k 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 ...
3
votes
2answers
411 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
1answer
20 views

Inverse Parameters of a Pan-Tilt Rotation Possible?

I have a 2-parameter (tilt,pan) rotation computed as tilt followed by pan, i.e. two rotation matrices multiplied together: $$R(t,p)=\begin{pmatrix} c_p & s_p s_t & s_p c_t \\ 0 & c_t &...
0
votes
1answer
18 views

Computing new 3D coordinates given time and linear velocity

Assume that an object in a 3D space has a position $\displaystyle {x}, {y}, {z}$ and a linear velocity $\displaystyle v_{x}, v_{y}, v_{z}$ Can I predict the new $\displaystyle {x}, {y}, {z}$ position ...
1
vote
1answer
36 views

Find all near points in a large array of points

Simplified problem: I have an array of points in 3D space. I want to find all pairs that are within a given distance from each other. (I'm writing a very simple simulation and the points merge into a ...
41
votes
14answers
76k views

Calculate Rotation Matrix to align Vector A to Vector B in 3d?

I have one triangle in 3d space that I am tracking in a simulation. Between time steps I have the the previous normal of the triangle and the current normal of the triangle along with both the current ...
0
votes
1answer
398 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 ...
0
votes
2answers
103 views

Convert direction vector to euler angles

How do I convert a direction vector to euler angles? I need to change the position of a character's head in a Java program that I'm writing. The pose of the head uses euler angles. I know the ...
0
votes
0answers
19 views

Calculating fov angle based on distance

I'm trying to calculate the angle between me and the target angle yaw in a 3D game, so that the actual angle is always the same based on distance how far I am from the target. I've tried a few ...
1
vote
1answer
504 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 ...
0
votes
2answers
28 views

Normal to surface at point

I have this function: $F(x,y,z)=x^2−y^2−z^2+4$ where $z\ge 0,0\le x \le 2,0 \le y \le 2$. How can I find the normal at some point $P=(p_x,p_y,p_z)$? I have tried to calculate the derivatives of ...
1
vote
0answers
15 views

Scaling in world space

In a hierarchical transformation system, where a node has one parent and children (Tree form) I want to scale an object with respect to world space axis. My transformation order is (Translate * Rotate ...
0
votes
0answers
17 views

Finding all three components (x, y, z) of a 3d vector using direction angles and the vector magnitude

I have the alpha, beta, and gamma direction angles of a certain vector. I also have the magnitude of this vector. These angles are being determined by a gyroscope mounted on a Quad-copter. Since ...
0
votes
0answers
16 views

Absolute value of an RBF distance is less than the absolute value of an actual distance

I have a radial basis function with a linear kernel f(r)=r in 3D. I constructed the surface based on this RBF and noticed that the absolute value of actual distance from any point to the constructed ...
2
votes
1answer
46 views

Finding the parameters of an ellipsoid given its quadratic form

Suppose we have the quadratic form of an ellipsoid of the form $$ax^2 + by^2+cz^2+dxy+eyz+fxz+gx+hy+iz+j=0$$ I want to find centroid of the arbitrarily oriented ellipsoid, its semi-axes, and the ...
0
votes
0answers
38 views

Equations of the tangent planes to the sphere

Find the equations of the tangent planes to the sphere $x^2+y^2+z^2-10x+2y+26z-113=0$ which are parallel to the straight lines $\frac{x+5}{2}=\frac{y-1}{-3}=\frac{z+13}{2}$ and $\frac{x+7}{3}=\frac{y+...
18
votes
6answers
29k views

Parametric Equation of a Circle in 3D Space?

So, my dilemma here is... I have an axis. This axis is given to me in the format of the slope of the axis in the x,y and z axes. I need to come up with a parametric equation of a circle. This circle ...
0
votes
1answer
21 views

Removing Discontinuity in 3-space without changing the partial derivative

Is it possible to find a version of the function $$f(x,y) = x\cdot \lfloor y \rfloor + \lfloor x\rfloor^2$$ That is continuous. ANY operation is allowed in changing the function as long as the ...
1
vote
0answers
20 views

Newtonian potential of homogeneous ball

Let $x \in B_R(0) \subset \mathbb{R^3}$. To compute $$u(x)=\int_{B_R(0)} \frac{1}{|y-x|} dy$$ The integrand has singularity at $x$, so consider $$u_\epsilon(x)=\int_{\substack{|y|< R \\ |y- x|> ...
1
vote
1answer
936 views

Fitting a line curve to 3D data

I have a set of points in 3D which I need to fit a curve (not a plane) to. Essentially these points describe a string with a set order (i.e. point one connects to point two, etc.) and I need to fit a ...
2
votes
3answers
14k views

How to find shortest distance between two skew lines in 3D?

If given 2 lines $\alpha$ and $\beta$, that are created by 2 points: A and B 2 plane intersection I want to find shortest distance between them. $$\left\{\begin{array}{c} P_1=x_1X+y_1Y+z_1Z+C=0 ...
1
vote
0answers
39 views

Proof that there exists a 3d representation of all graphs

Below is a question and proof that I've done. I was wondering if there is a more formal way of concluding a point must exist that is not in a set composed of a finite number planes. Currently I am ...
2
votes
4answers
63 views

The formula for 3D rotation of the perspective of an image in 2D space

Do you know what the formula is for the 3D rotation of the perspective of a 3D object in a 2D space. For example, imagine that we got a picture of a 3D object. So, we have the projected picture of ...
2
votes
1answer
445 views

Counting the number of cubes in an isometric view

I had seen questions in a sample aptitude test, where an isometric view of an object made up of cubes was given, with some of the cubes removed. We were supposed to count the number of cubes present ...
0
votes
1answer
628 views

Best fitting circle to points in 3D

I have a set of n ≥ 3 points in 3D that are measurements of a possible circle. The measured points are "noisy" so best-fitting algorithms are involved. I'm programming in C# and have put together some ...
0
votes
2answers
22 views

Formula For 3D Dilation?

If I have a sphere on a 3D grid with it's center being at the origin, and I want to double the size of the sphere, where would it's poles be?
0
votes
1answer
431 views

3D Vector defined by 3 angles trigonometry components

What I'm looking for is the trigonomery equations to calculate the x, y and z components of a 3D vector. What I mean: The counterpart formulas for a 2D vector defined by 1 angle: $x = \cos(\alpha)...
2
votes
1answer
567 views

Intersection of a line segment and a paraboloid in 3D

Suppose I have a line segment $L$ in 3D: $$x=a_1(1-t)+b_1t$$ $$y=a_2(1-t)+b_2t$$ $$z=(a_1^2+a_2^2-k_1^2)(1-t)+(b_1^2+b_2^2-k_2^2)t$$ Because $L$ is line segment then $0\leq t\leq 1$. And defining ...
2
votes
2answers
804 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.
1
vote
3answers
889 views

Identify and sketch the quadric surface?

I'm stuck trying to figure out which type of quadric surface this equation is: $$\dfrac{x^2}{16} - \dfrac{y^2}{9} - \dfrac{z^2}{1} = 1$$ I have narrowed it down to a hyperboloid, but cannot ...
1
vote
1answer
28 views

Efficient assignment of tetrahedron's chirality

Suppose we have a regular tetrahedron delimited by four points $A_{1}, A_{2}, A_{3}, A_{4}$. There are 24 permutations of vertices, but there are only two distinct terahedra that cannot be ...
2
votes
1answer
19 views

Non-trivial 3D curve that projects as a line or a segment onto the faces of the quadrant

I want to illustrate how high dimensional objects may have misleading projections. Examples are for instance given with HiSee software, with nD bouquets of circles. Are there non-trivial (not a 3D ...
1
vote
0answers
26 views

Translation by tensors

According to this question, quaternions would not be the right choice to handle both rotation and translation. In the case of tensors, one might assert that the rotation would be possible by tensors, ...
1
vote
1answer
15 views

3-Space Vertices of a Parallelogram

The points (1, -2, 4), (3, 5, 7) and (4, 6, 8) are three of four vertices of parallelogram ABCD. Explain why there are three possibilities for the location of the fourth vertex, and find the three ...
2
votes
1answer
28 views

Determining angle of view from an image with a square or checkerboard in the background.

I take a picture of a square of known dimension (let's say 1x1 units) with the camera at an unknown angle relative to the plane of the rectangle. (The distance to the rectangle is also unknown, but ...
1
vote
2answers
123 views

**Location** of shortest distance between two skew lines in 3D?

I can find the shortest distance $d$ between two skew lines $\vec{V_1}$ and $\vec{V_2}$ in 3D space with $d=\left|\frac{(\vec{V_1}\times\vec{V_2})\cdot\vec{P_1P_2}}{|\vec{V_1}\times\vec{V_2}|}\right|$...
0
votes
0answers
29 views

Counting balls in face centred cubic close packing

Possibly too easy for stack exchange, but... Consider a cubic close packing, or face centred cubic, arrangement of balls or radius $1$ in dimension $3$. Suppose that the origin is the centre of one ...
0
votes
1answer
74 views

Locus of the center of the circle of radius $a$,which always intersects coordinate axes

If the axes are rectangular, show that the locus of the center of the circle of radius $a$,which always intersects coordinate axes is $x\sqrt{a^2-y^2-z^2}+y\sqrt{a^2-z^2-x^2}+z\sqrt{a^2-x^2-y^2}=a^2$ ...
1
vote
1answer
49 views

Can there be a limit cycle without a fixed point in 3D space?

I am working with a population dynamics model. Basically, I have a nonlinear ODE in $R^3$ space, (X,Y,Z), and I know that if I start in the an open region ($0<X<1,0<Y<1,0<Z<1$, ...
0
votes
0answers
36 views

Euler Angle + Distance to XYZ coordinate

Background I'm familiar with Euler Angles and 3d space systems but I'm having trouble with Rotation Matrices. Scenario I've converted my Euler Angle to degrees for ...