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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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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56 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 ...
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1answer
685 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 ...
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2answers
630 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} + ...
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1answer
267 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 $P$ ...
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1answer
752 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? ...
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1answer
113 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 ...
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1answer
629 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
920 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 ...
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1answer
150 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 ...
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2answers
2k 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
784 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), ...
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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
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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.
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1answer
89 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 ...
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0answers
32 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 ...
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0answers
392 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} ...
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1answer
614 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 ...
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3answers
118 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} ...
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1answer
129 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 ...
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2answers
85 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 ...
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3answers
554 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 ...
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0answers
57 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
61 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 ...
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1answer
2k 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 ...
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3answers
1k 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, ...
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2answers
318 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 ...
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1answer
111 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 ...
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1answer
2k 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|\; ...
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1answer
269 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 ...
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1answer
944 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 ...
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1answer
421 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 ...
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1answer
628 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 ...
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0answers
303 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 ...
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1answer
8k 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 ...
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0answers
113 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
256 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 ...
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0answers
115 views

Determining pose of an object in 3d space

Given a 3D model of an object centred at the origin, if I place a camera at position (x,y,z) and make it face the origin, from the image rendered the object appears ...
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1answer
4k views

How to find an all-in-one 2D to 3D Transformation Matrix for perspective projection, rotation, and translation?

I have read Finding a 3D transformation matrix based on the 2D coordinates but I think my situation is different because I think I need a 4x3 matrix, not a 3x3 matrix. I'm not sure but this might be ...
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2answers
471 views

Angle between planes

If the angle between two planes is $\alpha$ , why is the angle between normal of the two planes is $\pi - \alpha$ ? Also Why angle between a line and normal to a plane is $\pi/2 -\alpha$ if angle ...
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0answers
760 views

calculate out-of-plane and in-plane rotation from virtual camera position.

I am trying to reproduce some work from an author which generates multiple views of a 3D object under different projections and labels each view with a 3D pose. The author states that they "place a ...
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5answers
359 views

Does this interesting property characterize a sphere?

Consider 2-d surfaces in 3-d (at the suggestion of a comment, let's say closed connected 2-dim smooth manifolds, embedded in dimension 3) with finite area. A sphere has the interesting property that ...
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0answers
186 views

Change of coordinates in 3D

It's been a while since my last geometry class and I need some help in solving a very simple problem I have. I need to implement a zoom function in 3D in a piece of software I am writing. My system ...
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0answers
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Higher-dimensional analogue of a cone point

If you look at the intrinsic geometry of a cone, there's a defect on the point of the cone known as a cone point. The only higher dimensional analogue I've heard of is what you get if you take the ...
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1answer
245 views

3D Road - Rotate around 3d curve

First of all, I'm not sure whether to post this on stackoverflow or here, but since there's some mathematics needed here (especially at the end of this question) I posted it here. I'm given a ...
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2answers
222 views

Software for visualizing partial derivatives?

I'm whipping up a set of notes, and I want to include a diagram or two showing some partial derivatives. Specifically, a diagram would include: a 3D surface of the form z=f(x,y), a plane of the form ...
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2answers
575 views

Kepler's First Law in 3D

Kepler's First Law in 2D polar is $$ r = \frac{p}{1 + \varepsilon\cos(\nu)}. $$ How can this be written to consider ellipses in ...
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1answer
265 views

Getting a 3d linear equation knowing the rotation of an object

I have an object, a simple rectangle I rotate it by a certain degree using Euler Angles, in this case around Z, to make it easy lets say it's 45 degrees. Right now I want the yellow: Y-Axis linear ...
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2answers
267 views

Given a 3D directional vector, and a 3D point, is it possible to calculate a 'rotation around the vector' for other points?

Sorry if the title if confusing. Essentially I have a vertex and a vector (the normal of a plane which the vertex sits on), and would like to be able to calculate the 'angle' along the plane of any ...
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1answer
40 views

Calculating transformation from origin to point

I have an icosahedron of radius $x$ with 12 vertices at known coordinates. If I have a point at $(0,0,x)$ where $x > 0$ and a vertex of this icosahedron at $(a,b,c)$ how can I find the rotation ...