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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40
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13answers
70k 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 ...
1
vote
3answers
88 views

Parametrization of the intersection of two given surfaces

Find a parametrization of the intersection between the two curves $z=x^2-y^2$ and $z=x^2+xy-1$. I figure I should set them equal to each other but I'm not sure where to go from there: $$x^2-y^2 = ...
1
vote
0answers
35 views
+50

Euler angle to direction vector which is right?

I tried to implement a first person shooter camera using Euler angles with the order pitch-->yaw rotation.(pitch is rotate round X axis, yaw is rotate round Y axis) Many tutorial gave the formula ...
0
votes
0answers
19 views

Parametric equations for a line perpendicular to two given lines.

We are given two lines in $\mathbb{R}^3$: $L1 : x = 4t , y = 1-2t , z = 2+2t;\\ L2 : x = 1+t , y = 1-t , z = -1+4t.$ The question asked was to find the parametric equations for the line that is ...
0
votes
1answer
15 views

Find volume of cube with the help of eqn of plane

The volume of cube whose two faces lie on the plane 6x-3y+2z+1=0 and 6x-3y+2z+4=0?
0
votes
0answers
12 views

Find tangent common tangent plane…

Number of common tangent planes to the sphere $(x+2)^2 +y^2 +z^2 =1$ and $(x-2)^2 +y^2 +z^2 =1$ that pass through origin.
0
votes
1answer
531 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
25 views

Find a point 90° left or right from a point (x,y,z) in a 3D space.

How can I find a point which is 90° left or right from a point (x,y,z) in a 3D space? for example if I have the point $(x,y,z)$ how to find $(x1,y1,z1)$ and $(x2,y2,z2)$.
0
votes
1answer
395 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 = ...
0
votes
1answer
49 views

finding two most distant 3d points

I'm trying to write an algorithm. There are $9$ points $3$ of $x$, $3$ of $y$, $3$ of $z$. How can I find the two most distant? Mathematically, I need explanation. Thank you for all appreciated ...
1
vote
0answers
23 views

Tricubic Interpolation

I am currently writing a plugin for 3D analysis software and I am working with a data grid where certain values are stored at XYZ coordinates, and I need to find an estimated value of a point that ...
1
vote
1answer
14 views

how to find the pivot/axis and angle that move one coordinates space to another?

I am writing a plugin for a 3d modeler, and I am stuck. For my plugin, I need to get the axis and the angle used for rotating a 3d object. But I only get the coordinates (~ 3dmatrices) of the objects ...
0
votes
1answer
12 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 ...
2
votes
1answer
29 views

Is there some relationship for all points on a rectangle?

For a line in 3D space, you can know that for each P on the line with endpoints A and B and length L, it holds that ||P-A|| + ||P-B|| = L My question is: is there a similar expression for points on ...
1
vote
1answer
18 views

Perform a rotation in 3D world

I got a character at some point $A$ facing to point $O$ that is equal to $(0,0,0)$, then I move it to point $B$ and I want to rotate him to face point $O$. Since this is 3D world I think that I need ...
0
votes
0answers
19 views

Slicing a 3d surface using a 2d line equation

So what I'm trying to do is to find the equation of a 2d function on a 3d surface using a 2d line equation. With : $z = f(x, y)$ the equation of the surface and $ax + by + c = 0$ the line ...
2
votes
2answers
8k 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
0answers
12 views

Progressively embed ( = superscribe?) and immerse …

$\mathbb R^1$ is superscribed/embedded on $\mathbb R^2$ and $\mathbb R^2$ in turn immersed in $\mathbb R 3$. Graph of a line $ x(u,v), y(u,v), z(u,v),f(u,v)=0 $ is superscribed or embedded on ...
2
votes
2answers
753 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
1answer
627 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
36 views

Geometric Optimization

In 1990 W. Kuperberg conjectured that it is impossible to have seven infinite mutually disjoint unit cylinders all touching a unit sphere. As a first step towards a solution I would like to answer the ...
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 ...
2
votes
1answer
547 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 ...
0
votes
1answer
45 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
0answers
25 views

Does 3D euclidean space allows vector sum in 2 dimensions?

Is this right to add two orthogonal vectors to to get one vector, using this vector in calculations and after getting results, decomposing result vector to get orthogonal components? I am a ...
2
votes
1answer
432 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
3answers
2k views

Find perimeter and angle of triangle using three 3d vectors .

Given the following, three vectors: $$\vec{a} = 3\mathrm{i} - 2\mathrm{j} + 5\mathrm{k}\\\vec{b} = \mathrm{i} - 6\mathrm{j} + 6\mathrm{k}\\\vec{c} = 2\mathrm{i} + 3\mathrm{j} - \mathrm{k},\\$$ find ...
0
votes
1answer
30 views

Angle between planes challenging Question

The plane $r.(a,3,5)=10$ is inclined at an angle of $45^\circ$ to the plane $r.(-5,1,4)$ Find the value(s) of $a$ up to $2$ decimal places. I attempted this problem by forming an equation where ...
1
vote
1answer
27 views

How to programmatically find dodecahedron's edges as couple of vertices

I'm a newbie here, and I'm not a mathematician, so I hope you could help me. Online I found that the 20 vertex of a dodecahedron can be easily expressed as: ...
1
vote
1answer
24 views

Finding the radius of a sphere inscribed in a right prism

We have right prism $ABCA_{1}B_{1}C_{1}$ and points $E$, $D$ such that: $A_{1}E:EB_{1}=B_{1}D:DC_{1}=1:2$ The distance between lines $AE$ and $BD$ is $\sqrt{13}$. Find the ...
2
votes
2answers
392 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
16 views

How to calculate rotation quaternion between two orientation quaternions?

I have some device (3D pointer) connected to my computer which returns it's position (in cartesian XYZ system) and orientation (in quaternions). I receive this values about 30 times/sec. Now I need ...
0
votes
2answers
69 views

Geometrical interpretation of solving a $3 \times 3$ system of equations

Solve the following system of equations and give a geometrical interpretation of the result. \begin{align*} x + y + z &= 6\\ 2x + y − 3z &= -5\\ 4x − 5y + z &= −3 \end{align*} I know that ...
2
votes
2answers
33 views

Calculating cosine of dihedral angle

Let $O,A,B,C$ be points in space such that $\angle AOB=60^{\circ},\angle BOC=90^{\circ},\angle COA=120^{\circ}$ Let $\theta$ be the acute angle between the planes $AOB$ and $AOC$. Find ...
1
vote
1answer
703 views

Intersection of Ellipsoid with Ray

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 ...
3
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 ...
2
votes
1answer
38 views

How to derive 2D equation representing minimums of constrained 3d equation?

I have a 3D (multivariate) function f(x,y) which can be represented as a surface with constraints. When the surface is viewed from the side (as below), such that the Y axis is not visible, there is ...
0
votes
0answers
10 views

What is the formula for a cone built from two arbitrary vectors?

Suppose there is an arbitrary vector in 3D space : $\vec v = (a,b,c)$ , starting from point $(x_0,y_0,z_0)$ which is the center or 'spine' of the cone. There is also the vector $\vec u = (h,i,j)$ , ...
5
votes
7answers
22k views

Find if three points in 3-dimensional space are collinear

Find if the points joining $A=(6,7,1), B=(2,-3,1)$ and $C=(4,-5,0)$ are collinear. How to determine collinearity in three dimensions? In two dimensions, one can compare the slopes of segments ...
0
votes
2answers
25 views

Calculate a normal to vector lying on a plane formed by $2$ vectors

Let's presume I have two vectors $V_1$ and $V_2$. As far as I understand normal to a vector is all vectors lying on a plane perpendicular to it. What I need is a normal to $V_1$ that lies on a plane ...
0
votes
1answer
27 views

Converting a 3D line's equation into vector form.

How exactly can I convert the below equation into the vector form? (i.e. V(i,j,k) form or $a*i+b*j+c*k$ form): $$\frac{x-5}{-10}=\frac{y-3}{-6}=\frac{z-2}{-4}$$ I'm actually trying to find the angle ...
0
votes
1answer
24 views

Find cone-plane intersection points in a construction

I have two points on the X axis, A and B, which are connected to the two points, C and D on the sketch plane parallel to XY plane. I have a point E which lies at distance h from D point in Y direction ...
1
vote
2answers
35 views

Confusion in Total faces in Cone: 3D

I have checked in many places about how many faces does a Cone have.. As per this link. There is 1 face in Cone As per this link, there are 2 faces in cone As per this Video, A Cone has one face ...
1
vote
1answer
15 views

Determine plane rotation in 3D when only knowing the length of it sides?

For an assignment in computer graphics, i need to be able to determine a plane's rotation by just holding it in front of my webcam. So basically I only got 2D coords of the plane's points. I searched ...
0
votes
0answers
10 views

Transformation of 3D vectors to other planes in 3D

Suppose I have a set of points A, B, C, D, E, F... defined by the 3D vectors AB, AC, AD, AE, AF, AG etc. I can describe the geometry of these by defining them in an arbitrary plane e.g. z = 0 ...
-2
votes
0answers
22 views

What is the number of levels in Qubrix Brain Twister?

Qubrix is essentially a derivative of the Rubik's Cube (Hungarian Cube), it consists of 9 cubes that are geared to each other in different ways, depending on the level. At the beginning cubes are ...
0
votes
0answers
20 views

Finding extremas of a function

$f(x,y) = xe^{-{x^3}+{y^3}}$ and I am to find extrema values of that 2-variable function. I come up with the point $P(3^{1/3},0,f(3^{1/3},0))$ is its only critical point. I tried to apply second ...
2
votes
2answers
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 ...
0
votes
2answers
41 views

Quaternion angle - Opengl rendering

I have been using a 6dof LSM6DS0 IMU unit (with accelerometer and gyroscope). I am trying to calculate the angle of rotation around all the three axes and Render a 3D cube using opengl to immitate the ...
1
vote
1answer
456 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 ...