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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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
268 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
110 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
96 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
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 ...
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3answers
344 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
35 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 ...
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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 ...
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3answers
739 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
238 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
75 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
831 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
188 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
453 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
288 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
262 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
164 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
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 ...
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0answers
74 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
139 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
78 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
2k 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
389 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
413 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
328 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
132 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
24 views

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
205 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
139 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
305 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
169 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
171 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
37 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 ...
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1answer
566 views

coordinates of icosahedron vertices with variable radius

I was looking on the wikipedia page about icosahedrons and it says that for edge length $a$ the radius of the circumscribed sphere around the icosahedron is given by $r = a \times ...
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0answers
113 views

Intersection of a hollow cone and a circular disc in 3D

I'm trying to calculate the area of a hollow cone intersecting a circular region on a surface. Basically a hollow cone is defined by its starting apex and its ending apex, the height of the cone from ...
2
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1answer
474 views

3-D generalization of the Gaussian point spread function

I would like to extend to 3-D the formulation of the 2-D Gaussian PSF, given by: $$k_{\sigma}(x,y)=\frac{1}{\sqrt{(2\pi)^2}\sigma^2}\exp\left[-\frac{x^2+y^2}{2\sigma^2}\right]$$ Is the following 3-D ...
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1answer
260 views

Interpolating missing points in 3D data-set

Given the following x,y,z points (z is actually a signal strength indicator in dBm): ...
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1answer
41 views

A triangular “spot function”

z = (cos πx + cos πy) represents the classical "spot function", made by square cells, used in every laser printer's halftone screening. Does anyone knows the corresponding function to produce ...
2
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0answers
57 views

Finding a simple template within a 3D point cloud

I want to find a template - defined by 5 coplanar, non-collinear points - within a point cloud of say 100 3D points, in the most efficient way possible. I know there is the ICP (Iterative Closest ...
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0answers
92 views

Mapping an object's projected 3D path to a pre-defined top-down 2D path.

The title of the question may be misleading and the context simpler. Please suggest more appropriate tags for this question. Consider looking at a plane from two different perspectives. Perspective ...
0
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1answer
182 views

Ear clipping triangulation snip calculation

I have a working code of 2D triangulation of a polygon. This uses the following code to detect if a triangle is actually an ear: ...
2
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0answers
110 views

RANSAC line fitting (3d) by line segments (3d)

I am having many 3d line segments. some of them are nearly parallel and some are oriented in to different direction. I want to avoid outliers and to get the best line 3d to represent the given ...
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0answers
97 views

Mathematical Basis for Dimetric Projection

For a school project, I need to make a program that can plot $y = f(x,z)$ using a form of dimetric projection. I was given the projection formulae $$\begin{align*} x' &= x + sz\cos(\theta)\\ y' ...
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1answer
292 views

Goldberg polyhedra coordinates

I would 3D-print some Goldberg Polyhedra importing in Sketchup, the coordinates provided on these links: 72 faces (2,1) - (coordinates) 132 faces (3,1) - (coordinates) 192 faces (3,2) - ...
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1answer
485 views

Angle between different rays (3d line segments) and computing their angular relationships

I have several positions (say A,B,C,..) and I know their coordinates (3d). From each point, if a certain ray is passing in a way to converge them at a given (known) point (say O). This point O ...
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1answer
53 views

Generate a Normal in 3D Without Branching?

I have a vector $v$ in arbitrary 3D space ending at point B. In order to generate the next point -- C, I uniformly pick an ...
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2answers
254 views

Vector Picking on the Unit Sphere

Imagine a vector from the center of a unit sphere to its surface: Now imagine a second vector generated in indentical fashion. Given the first vector, how can I generate vectors to uniformally ...
2
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1answer
88 views

3D Geometry Question

In $3$-dimensional Geometry, if angle made of line segment $OP$ with $X,Y,Z$-axis are in $1:2:3$, then what is the angle made by line segment with $Y$-axis? My Solution: Let $\alpha,\beta$ and ...
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3answers
66 views

A plane is raise 8 inches in the front and lowered 8 inches in the back, how much does the tip of a perpendicular rod on the plane move?

The image above shows the situation. There is a 2 foot long plane (width unknown) with a 3 foot high rod in its center perpendicular to the plane. and the plane in moved up 8 inches at the front, ...