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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2answers
71 views

What's the mathematics behind 3D modelling? [on hold]

I'm highly interested about 3D modelling in software, and I know that it has some deep mathematics behind it too. I would like to learn what specific topics are behind it mathematically. As long as I ...
0
votes
0answers
9 views

Mathematical theory for equally distributed dipole structures with inner equilibration

I'm looking for a mathematical theory for equally distributed dipole structures with inner equilibration. I know, that there exist two magnetic clusters, where the north and the south poles equally ...
0
votes
1answer
23 views

Size of a 3D object with relation to reference point [on hold]

I have a simple image of a table. I placed a reference ($10 \times 10$ rectangle) on top of it. I know the size of the rectangle and I want to calculate the size of the table. If I try simple ...
0
votes
1answer
404 views

How you could you change the surface area formula for a cylinder to calculate the curved surface area of the half pipe?

Skateboarders use half pipes for doing tricks. A half-pipe is a half cylinder. Explain how you could manipulate the surface area formula for a cylinder to calculate the curved surface area of the ...
2
votes
1answer
525 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
660 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
11 views

How to find a point which lies at distance d on 3D line, given a position vector and direction vector?

I have a position vector $(p_x, p_y, p_z)$ and direction vector $(v_x, v_y, v_z)$. I need to find a point on along the direction vector which is at distance $d$ from $(p_x, p_y, p_z)$.
1
vote
1answer
20 views

Motion in 3D Space: Finding Velocity from Distance, Launch Angle

The question asks: A bullet is fired from the ground at an angle of $45°$. What initial speed must the bullet have in order to hit the top of a $130 m$ tower located $190 m$ away? (Recall that ...
0
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2answers
20 views

Find the equations of $x-y$, $x-z$ and $z-y$ planes.

Do the $y-x$ and $x-y$ planes have the same equations? I think that the equation of the $x-y$ plane can be $x+y+z=0$ or $x+y+z=4$ or $ax+by+cz=$ any real number and $a,b,c$ are arbitrary real numbers. ...
-1
votes
0answers
20 views

Converting two points in 3D to a vector [on hold]

I'm writing code that reads a NEC-style card deck and displays it in 3D. I'm utterly noob to 3D, so insert joke here. The main part of this data are "wires" defined as two (x,y,z) points in 3D. My 3d ...
1
vote
1answer
45 views

Conjugating rotation by another rotation

If $g ∈ \mathrm{SO}(3)$ is the rotation about axis $p$ by angle $α$, and $h$ is a rotation mapping $p$ to another line $q$, then $g$ conjugated by $h$ is the rotation about $q$ by the same angle $α$. ...
1
vote
0answers
52 views

Rotation of point with infinite child objects. (Chain rotation)

More of a thought experiment here, knowledge for knowledges sake. Let's say you can create infinite points that rotate smoothly and at the same speed as each other through a full revolution - let's ...
2
votes
2answers
28 views

Extracting the Axis a Quaternion is rotating around from the Quaternion itself Directly

Quaternion has components X, Y, Z, and W. If you created a Quaternion with input being a 3D Vector representing the axis (X,Y,Z) and a floating point number representing the amount to rotate around ...
1
vote
1answer
56 views

Quaternion - Angle computation using accelerometer and gyroscope

I have been using a 6dof LSM6DS0 IMU unit (with accelerometer and gyroscope). And I am trying to calculate the angle of rotation around all the three axes. I have tried may methods but not getting the ...
0
votes
0answers
18 views

How to rotate a 3D object, using only local x-, y-, and z-rotations, so that it always faces a camera at the origin

I have been struggling with a difficult problem involving 3D rotations. I first came across this problem in a computer science context, but I've attempted to generalize it a bit before posting. (I ...
1
vote
2answers
31 views

Find the projection of the line $x+y+z-3=0=2x+3y+4z-6$ on the plane $z=0$

Find the projection of the line $x+y+z-3=0=2x+3y+4z-6$ on the plane $z=0$ The equation represents the line of intersection of two planes. Using augmented matrix $$ \begin{bmatrix} 1 & 1 ...
2
votes
1answer
32 views

Equation of plane perpendicular to given plane

Find the equation of the plane which contains the line of intersection of the planes $x+2y+3z-4=0$ and $2x+y-z+5=0$ and which is perpendicular to the plane $5x+3y-6z+8=0$ By setting $z=0$ I found a ...
0
votes
3answers
49 views

How do I compute the angles of a pyramid from the angle between its sides?

I have been given the following problem to solve: In a right pyramid whose base is an equilateral triangle, the angle between 2 side-faces is 70 degrees. Compute the base angle of a side-face. I ...
-3
votes
2answers
35 views

How to determine that the 3 points given in homogeneous coordinates are collinear? [closed]

How do I prove that the 3 points given in homogeneous coordinates are collinear? $$A=(1,3,2)^T, B=(0,6,8)^T, C=(3,3,-2)^T$$
1
vote
1answer
19 views

Rotation matrix between two similar cuboids using their upper sides ( and the planes defined by these sides)

I have two different images and with them an estimation of two planes ( defined in the same system). I would like to get the rotation matrix, quaternion or euler angles of a surface within this ...
0
votes
1answer
48 views

Plane rotation: range of angles to produce all posible x'y' planes

Given an $(x, y, z)$ system I create a new system $(x', y', z')$ by applying two rotations $\theta$ and $\phi$. In the new system the $(x',y')$ plane, i.e.: the $z'=0$ plane, can be written as: $$ ...
1
vote
2answers
89 views

Gradient of an angle in terms of the vertices

Let $\theta(\vec p, \vec q, \vec r)$ be the angle theta between 3D real vectors $(\vec{q}-\vec{p})$ and $(\vec{r} - \vec{p})$. What is a simple expression of $\nabla \theta$ in terms of $\vec{p}$, ...
1
vote
1answer
20 views

Equation of line passing through origin

Find the equations of the two lines through the origin which intersect the line $\frac{x-3}{2}=\frac{y-3}{1}=\frac{z}{1}$ at angles of $\frac{\pi}{3}$ Now our required line should be ...
0
votes
0answers
17 views

Translate Pitch and Roll Angles of Object to those at different Yaw

I have been trying to find a method to translate the pitch and roll angles of one object to those of another connected object at a different yaw - i.e I have an IMU mounted on a quadcopter frame and a ...
3
votes
1answer
865 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 ...
4
votes
3answers
180 views

Volume of overlap between two convex polyhedra

I have two convex polyhedra represented by triangle meshes. I can easily determine if they are in contact or not, but when they are in contact then I would like to determine the volume of their ...
1
vote
3answers
115 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 ...
0
votes
1answer
555 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
40 views

$Z$ coordinates disappear in the general rotation transformation matrix.

I wanted to generate the general rotation transformation matrix ($3D$). But when I did the multiplication the result didn't include the original $Z$ coordinates,I don't know why the $Z$ disappeared. ...
0
votes
0answers
17 views

finding pixel coordinates

I'm trying to calculate pixel coordinates of 3d points Xw = [150 200 350] where R is given as \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ ...
2
votes
1answer
31 views

Calculate sphere radius using two vector points.

Using accelerometers I have acquired two $3D$ vectors $V_1$, $V_2$ which both have $(x, y, z)$. Assume that these vectors are points ($P_1$ and $P_2$) on the surface of a sphere ($S$), so that the ...
0
votes
1answer
33 views

Does $(x,y,z) = (2,1,1) +s(-1,-1,-1) + t(2,-2,-2)$ represent a line or plane?

Does the equation $$(x,y,z) = (2,1,1) +s(-1,-1,-1) + t(2,-2,-2)$$ represent a line or plane? I claimed it is a plane, as the two direction vectors are not multiples and thus for any values of $s$ and ...
2
votes
0answers
9 views

Vector equation of line containing point and perpendicular to plane [duplicate]

How would one find the vector equation of the line that contains the point (x0, y0, z0) and is perpendicular to the plane Ax + By + Cz = D?
0
votes
1answer
30 views

Give a geometric description of the following set of points

Give a geometric description of the following set of points: $x^2 +y^2 + z^2-8x+14y-18z>/= 65 $ So I completed the square and got the set to read: $(x-4)^2+(y+7)^2+(z-9)^2>/= 211 $ However ...
0
votes
0answers
36 views

can every object be represented mathematically?

I was just wondering if all 2D/3D objects/images/shapes could be represented by equations. For example, SpongeBob 2D curve and many more. How should I approach, as in, some theories that already ...
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 ...
3
votes
2answers
55 views

Pizza Delivery along the shortest path

You are the Captain of the USS Gauss and you have been flying in the direction $2 i + j + k$ for quite awhile. You are currently at the point $(6, 3, 3)$. Your helper monkey Mojo just ...
2
votes
1answer
29 views

rotation to quaternion matrix handeness

I've understand that quaternions do not have handness but rotation matricies derived from unit quaternions does. The following formula is given by wikipedia for quaternion to rotation matrix ...
4
votes
1answer
70 views

Complement of a knot that *isn't* rationally null-homologous

Let $K$ be a knot in a closed, oriented 3-manifold $Y$. It is a standard fact that if $K$ is (at least rationally) null-homologous, then $H_1(Y-K;\mathbb{Z})$ is isomorphic to $H_1(Y;\mathbb{Z})\oplus ...
7
votes
7answers
12k views

How to find the distance between two planes?

The following show you the whole question. Find the distance d bewteen two planes \begin{eqnarray} \\C1:x+y+2z=4 \space \space~~~ \text{and}~~~ \space \space C2:3x+3y+6z=18.\\ \end{eqnarray} ...
2
votes
4answers
53 views

Plane of intersection of two spheres

What is the plane of intersection of spheres $$x^2+y^2+z^2+2x+2y+2z+2=0$$ and $$x^2+y^2+z^2+x+y+z-\frac{1}{4}=0$$ I am not sure of how to do this, i just subtracted the two equations and i got a ...
0
votes
1answer
30 views

Trouble understanding solution to exercise

Given: Right tetrahedron, find $\angle \alpha$, between surrounding edge(not sure if this is the right term in English, but those edges is AD, BD and CD). and the plane of the base, and $\angle ...
1
vote
0answers
995 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
2answers
5k 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 ...
2
votes
1answer
386 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
20 views

Calculating rotations required to

I have a situation similar to a question asked on StackOverflow with the following image: I have an object that rests at the tip of the green arrow (point XYZ), and I'm using the following formulas ...
0
votes
1answer
25 views

Geometry problem with rectangular parallelepiped

Given right angled parallelepiped $ABCDA1B1C1D1$, with bases $ABCD$ and $A1B1C1D1$, which are squares with side $1$. if $\angle (B1C;D1A) = 60^\circ$ find the length of the surrounding edge (I'm not ...
0
votes
0answers
13 views

Project 4 cones onto a sphere

I have four cones. The angle of each cones is 140 degree. I need to project it onto a sphere(place it ) such that, the cones cover the maximum area with minimum overlap. I initially thought that ...
0
votes
1answer
34 views

Trouble with understanding a solution to an exercise

Given right triangular prism $ABCA_1B_1C_1$, the surrounding edge(not sure if this is the right term in English, but the surrounding edge are $AA_1, BB_1, CC_1$) are equal to $\frac{\sqrt{5}}{5}$ and ...
1
vote
1answer
39 views

What is the initial velocity height of a projectile with destination vector D and gravity G?

I am doing a modification of Unreal Tournament 1999. Normally the game's jump pads' velocity applied to pawns that reach it's radius is defined by a velocity vector, which is a true pain to change and ...