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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0answers
214 views

how to calculate the volume of irregular shape by the Cartesian coordinates of its corners?

I've 4 points in a plane "A" and another 4 in another plane "B". is there a way to automatically calculate the volume contained into this irregular box? The automation is important as this set of 8 ...
0
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1answer
205 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 ...
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2answers
1k views

What are the coordinates of the vertices of a regular tetrahedron, relative to its centroid?

I am trying to draw an equilateral/regular tetrahedron in Processing (subset of Java), so I have to define 4 triangles that meet at the 4 vertices. I have been able to find the coordinates for the ...
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0answers
52 views

determine the position of axis in 3d space

I added a picture here for the challenge of the day! I have a coordinate system (Xg, Yg, Zg) marked in blue color, and I want to determine their positions in the space (Xf, Yf, Zf). Those are unit ...
0
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2answers
216 views

Find Rotation Matrix to rotate axes and move coordinates of point from P0 to P1

I have a point $P_0 = [x_0, y_0, z_0]'$. I want to rotate the axes so that the new coordinates will be $P_1 = [x_1, y_1, z_1]'$. Define the following rotation matrices: $R_x = \left[\matrix{ ...
1
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1answer
59 views

Geometric interpretation of plane

What is the geometric interpretation (coincidence/parallel/intersection) of plane equations, x-2y+z=-1, 2x+y-3z=3, x+8y-9z=9 ?
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0answers
66 views

Find an SO(3) matrix which satisfies some linear constraints

I have the following optimization problem: $\displaystyle \min_R \sum_{i=1}^n (X_i^T R Y_i)^2$ where $R \in \text{SO}(3)$, i.e. is a 3x3 rotation matrix, and $X_i,Y_i \in \mathbb{R}^3$. If $n \le ...
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1answer
76 views

Determine if a point is contained in the circle in 3d space

I have a problem where I need to determine if a point is contained in the area of a circle in 3d space. For my circle, I have the radius (R), the position of the center (C) and a normal vector to the ...
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0answers
45 views

Equation of ellipsoid given foci and two semi-axes

How does one find the equation of an ellipsoid given two foci, $(a,b,c)$ and $(d,e,f)$, and one semi-axis $l$? $c$ may not be equal to $f$.
0
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2answers
365 views

Find equation of the circular cross section of a unit sphere

I have a unit sphere in Cartesian coordinates: $x^2 + y^2 + z^2 = 1$ or in spherical coordinates: $x = \rho \sin(\phi) \cos(\theta)\\ y = \rho \sin(\phi) \sin(\theta)\\ z = \rho \cos(\phi)$ I ...
1
vote
1answer
63 views

Calculate the center point of multiple lines

I have $n\ge3$ lines $L_i$ given in 3D Space. How do I calculate a point $P$ with minimal $\sum_{i=1}^{n} distance(L_i, P)$?
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1answer
56 views

3D coordinate Transformation

I am currently trying to align two bodies which do not have similar sizes and shapes. But both of these two bodies share some keynodes(similar nodal position with 0.1% error difference). How can I ...
0
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0answers
135 views

Calculating 3D points corrds from 2D image

The current scenario I have is that I have an image of a retangular board from an angle and I need to calculate the 4 corrdinates of the 4 corners of the rectangle. Currently I have gone through the ...
0
votes
1answer
687 views

Determine if projection of 3D point onto plane is within a triangle

In 3D, given three points $P_1$, $P_2$, and $P_3$ spanning a non-degenerate triangle $T$. How to determine if the projection of a point $P$ onto the plane of $T$ lies within $T$?
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1answer
52 views

3d Transformation

I am trying to understand 3d-transformation in html5, but can't understand how we get new (x1, y1) coordinates. For example, we have a plane on our screen with a point at coordinates (287, 431). We ...
0
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1answer
308 views

4D to 3D projection

Im trying to calculate the position of 4D point in 3D world. I started with 2D and tried to extend it to the 3D and then to 4D. Firstly, I found out that its easy to calculate the projected position ...
0
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2answers
194 views

If a line makes angles $\alpha, \beta, \gamma$ with the $x, y, z$ axes, then $\sin^2{\alpha} + \sin^2{\beta} + \sin^2{\gamma} = 2 $

The following is the question in my textbook:- If a straight line makes angle $\alpha$, $\beta$, $\gamma$ with the $x, y, z$ axes respectively, then show that $\sin^2{\alpha} + \sin^2{\beta} + ...
0
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1answer
49 views

Finding coordinates of closest approach

Given two lines $l_1=\mathbf E_1+k\mathbf E'_1$ and $l_2=\mathbf E_2+\mu\mathbf E'_2$ in 3D, there exists a shortest distance between the two lines. How does one find the coordinates of the points $P$ ...
3
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1answer
383 views

Triangle Point Picking in 3D

To take random uniform points inside a triangle Triangle Point Picking method is used. But this is for 2D points, how can I take random points from a triangle that is defined by 3 arbitrary 3D points? ...
0
votes
1answer
98 views

Eigenvectors for the equation of the second degree and right-hand rule

I'm trying to find the Eigenvectors for the equation of the second degree (for example Elliptic cone). The estimated values $V_1$, $V_2$ and $V_3$ must satisfy the right-hand rule. How can we verify ...
0
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1answer
433 views

Explain 3d transformation matrix…

In programming language like css, there is a 3d matrix. https://developer.mozilla.org/en-US/docs/Web/CSS/transform-function#matrix3d() Though, i don't know matrix or matrix3d. I have tried to learn ...
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2answers
661 views

Rotation in 3D (coordinate system transformation)

How do I rotate a point around point [0,0,0] in 3D. In picture I draw specific situation for illustration. At first I know point G[x,y,z] and I will tranfer it on axiz Z, where distance to center is ...
1
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1answer
105 views

Why are the axis labelled as such in the 3d Cartesian coordinate system?

A long time ago I was taught that in 3d space, the x axis is the length/width or left/right space, the y axis is the height, and the z axis is the depth. When we draw things in 2d on a page, this ...
3
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2answers
1k views

Form a Parallelogram by 4 Points

This is a question from my school. The following is the whole question. The vertices of a triangle $A$, $B$ and $C$ are given by the points $(-1, 0, 2)$, $(0, 1, 0)$, $(1, -1, 0)$ respectively. ...
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4answers
301 views

How do you find the area of a triangle in a 3D graph?

How do you find the area of a triangle in a 3 dimensional graph? Is it any different than a regular 2d graph? How would you solve it, if these were your three points? A(1,-4,-2), B(3,-3,-3), ...
2
votes
1answer
41 views

Question about reexpressing the dot product

Suppose that I have two arbitrary 3-dimensional vectors, $\vec{a}$ and $\vec{b}$. By the definition of the dot product, I can write $$\vec{a} \cdot \vec{b} = \left|\vec{a}\right| ...
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0answers
17 views

to find the radius of the sphere [duplicate]

I tried like: here slant height $l={h\over\sin 60}$ and radius of the base of the cone $R=h\tan 60$ but I am not able to find the radius of the sphere.
0
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1answer
82 views

$n$-dimensional rotation along a 2D arbitrary plane

Given two vectors in $\mathbb{R}^n$, $v_0$ and $v_1$, which define a plane including the origin a rotation along that plane can be defined from $v_0$ to $v_1$. I know the formula for rotation within ...
1
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0answers
30 views

sweeping edges till they get a given elevation on an oblique plane

I am constructing wireframe model of 3d objects (prisms,..etc.). from a triangular mesh, I have obtained boundary points and fit striaght lines in order to get polygon edges refering to prism ...
0
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0answers
262 views

Determining rotation axis for matrix with complex eigenvectors.

I'm using Zhang's method to determine the 3D camera parameters from a set of images. When calculating extrinsic parameters for the third image, I get the following matrix. $$ \begin{vmatrix} ...
3
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1answer
314 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
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3answers
111 views

In $\mathbb{R}^3$ find the equation of the circle passing for three points.

So, I have the following points: $\left( \begin{matrix} 5 \\ 0 \\ 0 \end{matrix} \right), \left( \begin{matrix} 0 \\ 4 \\ -1 \end{matrix} \right), \left( \begin{matrix} -4 \\ 4 \\ 3 \end{matrix} ...
0
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1answer
97 views

Normalizing a 3D angle distribution

I'm having trouble finding the proper keywords to search for this type of treatment so I apologize in advance if this is quite obvious. I have a collection of lines in 3D space approximately centered ...
0
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2answers
81 views

Finding the the radius of a sphere

I'm having a hard time to find the radius of this sphere equation. I got the center correct, but I can't get the correct answer for the radius. I'm completing the square, but my solution is off. I ...
0
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3answers
358 views

3D Trig Question?

I've been having trouble with this question: David is in a life raft and Anna is in a cabin cruiser searching for him. They are in contact by mobile telephone. David tells Anna that he can see Mt ...
0
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0answers
36 views

Folding a selection of points over the corners of a 3D cube

Already posted this question with some c# on stack exchange, but this question could probably be solved with smarter math then I can conjure up. Same Question on Stack Overflow Size of Cube is 6 x ...
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0answers
52 views

Are there algorithms related to cloud shapes?

This is going to be applied in programming, but I thought the question would be best answered here, since I'm just looking for algorithms at the moment. I'm generating clouds on the fly, but I'm not ...
1
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1answer
1k views

Angles projected to planes between two lines, one of which is in rolled 3D coordinate system.

Let's define standard 3D cartesian coordinate system XYZ. In the system define a line that: has a (0, 0, 0) point lies on the YZ plane has defined an angle between itself and Z axis (lets call this ...
2
votes
3answers
776 views

How to check if point is within a rectangle on a plane in 3d space

Please refer to this image for this question-> I have a 3d bounded box (in green). I also have a 3d line (in red) I know the points a, b, c, d, e. They are points in space with x, y, z, ...
0
votes
2answers
245 views

get a rotation matrix from an oriented vector quicker than Euler

I'm in $R^3$ and I have a solid 3d object and a vector, I would like to rotate and orient the solid according to this vector. I found that the simplest way to do that is to use euler angles, the ...
0
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1answer
76 views

Fitting a hyperboloid to 3 different radii

I would like to fit a hyperboloid to a set radii, but I must be making some mistake in solving for my derived constants. The question is technically only two-dimensional in nature, but I'm using a ...
1
vote
1answer
880 views

Angle between line and a plane

I want to calculate the angle between the plane with a normal $N = [N_x,N_y,N_z]$ and the vector $V = [V_x,V_y,V_z]$ and I used this formula for angle $$\alpha = \arccos \frac{V \circ N} {|V|\; ...
1
vote
1answer
192 views

sketching regions of three variables

If i had a solid region, V, such that $x^2+y^2+z^2\le9$, $x^2+y^2\le4$, $x\le0$ and $z\ge1$ what would be the easiest method to sketch this region? Can someone run me through steps as how to tackle ...
0
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1answer
482 views

Given a point (x,y,z) and an angle/bearing distance calculate the end point (x,y,z)

I'm not very mathematical but I'm working on a 3d program and for this part I simply want to draw a line. I know the starting vector (x,y,z), the length r of the line and the bearing/angle. I want to ...
0
votes
1answer
309 views

How do I determine the Tait-Bryan angles (yaw, pitch, and roll) of polyhedron faces to its center?

I'm modeling a pentagonal hexecontrahedron by placing faces and then rotating them. I've determined the center of each face by using the Cartesian coordinates of the vertices of its dual polyhedron ...
2
votes
1answer
277 views

How do I find the outline resulting from the intersection of a NURBS surface and a plane?

The context for this question is 3D printing. Currently the way it's done is: Convert a 3D model to a mesh of triangles Ensure it's manifold and that there are no degenerate triangles 'Slice' this ...
3
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0answers
171 views

Maximum length of pencil in a pencil case

What is the maximum length of an unsharpened, cylindrical pencil inside an empty rectangular pencil box? Or, in a rectangular cuboid of dimensions $x \times y \times z$, what is the maximum possible ...
0
votes
1answer
4k views

Angle between two 3D lines

I know for given 2 vector $\vec{u},\vec{v}$ the angle between them achieved by - $$\cos{\theta} = \frac{\vec{u} \cdot \vec{v}}{\|\mathbf{u}\|\|\mathbf{v}\|}$$ but what if I want to calculate the ...
0
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0answers
76 views

3D vertices $\rightarrow$ 2D polygon $\rightarrow$ 3d transformation

This may be a little strange. I have an array of 3D vertices, which represent a 3D face (n-gon). I first need to describe the face in 2D. I can then apply these transforms on it. X, Y, and Z ...
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3answers
143 views

Sample of a subset of a plane

I have the equation of a plane $ax+bx+cx+d$ and a point $(x_0, y_0, z_0)$ on that plane. I defined the neighborhood of that point on that plane as the set of points satisfying $(x-x_0)^2 + (y-y_0)^2 ...