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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Polarity of the Surface Normal of a 3D triangle

I have a triangle (defined in 3D space) that has 3 points (p1, p2 and p3). Is it possible to work out what the polarity of the surface normal would be for the face knowing it lists each point in an ...
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2answers
253 views

Gram-Schmidt Orthogonalization - does it distort?

I am writing a 3D solar panel positioning programme and have a section of code where I use the Gram-Schmidt Orthogonalization process to go from 3D to 2D for easier calculations. (For reference, here ...
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1answer
448 views

Uniform distributions on the space of rotations in 3D

I believe on moral grounds that the following three definitions are equivalent, and determine "the" uniform distribution on rotations in three dimensions. The Haar measure on $SO(3)$. The uniform ...
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1answer
359 views

how to get rotation component of quaternion form using 3d coordinates

I have a series of 3d coordinates distributed in a 3d space according to a root point. I can determine the x, y , z component using reducing the vectors. but I am not clear how to get rotation ...
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1answer
2k views

How to calculate the rotation matrix between 2 3D triangles?

I need to calculate the rotation matrix and the translation vector between 2 given triangles in Euclidean space. This is really just a rotation and a translation, the lengths of sides of the triangle ...
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3answers
2k views

Given a tetrahedron, how to find the outward surface normals for each side?

Say I have a triangle in $3$D space. I can get the surface normal by calculating the vector cross product of two of the edges. But, lets say I make this a tetrahedron. How can I work out the outward ...
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1answer
246 views

How to recover three successive rotations of a vector

I have a vector, which I rotated with respect to $x$, $y$ and $z$ axes, respectively. Now I want to recover this operation, that means I want to bring it to the previous position by rotating it with ...
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0answers
652 views

Calculating normal vector to a rotated plane

Forgive me if this isn't well phrased, it's been a while since I've done any maths! I have a 2d image whose central point is located at the world origin, and it is in the plane $z = 0$. If I rotate ...
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1answer
500 views

Calculating the norms of a triangle based pyramid

Hi I have the following co-ordinates, which make up my triangle based pyramid. I need to calculate the normals of each face. However Im struggling to find the best simplest way to do this? ...
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9answers
44k 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 ...
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2answers
3k views

Calculate distance, knowing actual and perceived size

What's equation would I use to calculate distance to an object, if I know it's actual and perceived size? Say there is a line, and I know it's actual length is 65 (units), I perceive it as 62 ...
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1answer
3k views

Rotating a plane in 3D Space

I have a plane defined by 3 points. I want to rotate that plane so that it will be possible to change the orientation of the plane in any dimensions. For example, what I want to do is converting this: ...
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3answers
862 views

Calculating start/end points of a line segment given by a set of points and normal direction

I have a set of $3$D points representing a line segment. Points are not equidistant distributed on the line segment. Points are also unordered. I also have the center point and the normal to the line ...
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1answer
160 views

Distance between point and line

Using the formula from this page: http://mathworld.wolfram.com/Point-LineDistance3-Dimensional.html how can you find the individual x,y, and z distances? I'm trying to figure it out but can't wrap my ...
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1answer
617 views

General solution for 3D line intersection

I've been trying to get the intersection point of 2 3D lines (in general, so i can code an algorithm) using the following equations: $$ x_0 + k_0 a_0 = x_1 + k_1 a_1 \tag{1}$$ $$ y_0 + k_0 b_0 = y_1 ...
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0answers
226 views

Quaternions in olympiad 3d geometry

It's known that we can use complex numbers to solve some 2d problems easier than synthetic methods. But, what do you think about using complex numbers in 3d geometry? I've found extend of complex ...
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0answers
461 views

Fitting a 3d point cloud with a polynomial surface

I have 3D point cloud and I would like to fit a polynomial surface to it. Could anybody please explain the step by step process to that. Thanks a lot.
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3answers
1k views

3D to 2D rotation matrix

I have been trawling through this forum but am struggling to understand the maths a bit. Currently I have a 2D plane within a 3D space and I have the coordinates for them. I want to work on this 2D ...
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1answer
198 views

Z-index of an arbitrary point on a flattened 3-dimensional triangle

I have a triangle in a 3-dimensional coordinate system that I want to draw to a screen. I'm able to flatten the triangle to 2 dimensions and determine whether an arbitrary point on the screen falls ...
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1answer
156 views

Using a Bivariate Gaussian Distribution to Predict Range of Movement

I am currently attempting to use a bivariate normal distribution to identify the most likely range of movement for a blob in computer vision. This itself is not the problem, however; I do not ...
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2answers
3k views

Rotate a 3D vector on a plane

I have a 3D line vector with end points x0 and x1, which lies along the x-axis of a subsection of the plane, ...
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2answers
9k views

How to transform a set of 3D vectors into a 2D plane, from a view point of another 3D vector?

I googled around a bit, but usually I found overly-technical explanations, or other, more specific Stackoverflow questions on how 3D computer graphics work. I'm sure I can find enough resources for ...
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1answer
260 views

calculate surface normal with random sampling of points

Given a surface in $R^3$ and a point P on the surface, I want to calculate the surface normal in this point, the vector that is perpendicular to the surface. However, I do not know the whole surface, ...
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1answer
674 views

The volume and surface area of pipe?

A line segment turns around a curve with right angle from point A to point B. I would like to find the closed region volume and surface area that figured out in the picture. Could you please give ...
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1answer
506 views

Calculating the rotations necessary to make a 2D object match the perspective of a plane in 3D space

I'm working with 3D rotations and extrusions in Adobe Illustrator. I have a square that I have extruded into a rectangular prism, which I've then rotated a known amount (x°, y°, z°) on each axis. I'm ...
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0answers
138 views

Transform 3D vectors between planes using a matrix

I've got 6 points in 3D space: $A,B,C,D,E,F$, that represent 4 vectors. $AB$ is perpendicular to $AC$ and $DE$ is perpendicular to $DF$. I need to find a transformation matrix M, that transforms $AB$ ...
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0answers
486 views

How to convert Yaw, Pitch, Roll and Acceleration value to cartesian system?

I am having readings of Yaw, pitch, Roll, Rotation matrix, Quaternion and Acceleration. These reading are taken with frequency of 20 (per second). They are collected from the mobile device which is ...
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1answer
861 views

To find the volume of tetrahedron by using all surfaces areas?

I am looking for a formula: $V=f(S_1,S_2,S_3,S_4)$, where $S_1$, $S_2$, $S_3$, and $S_4$ are the areas of the four faces. We know ...
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2answers
846 views

3d transformation two triangles

I have two triangles in 3d. I need to calculate transformation matrix(3X3) between two triangles in 3D. 1)How can I calculate the transformation matrix(rigid) while fixing one of the points to the ...
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1answer
526 views

Regular polygons that touching to a sphere surface

What is the possible number of n sided polygons(every face is the same regular polygon) that touching their corners to sphere surface and also touching each other ? I would like to know the relation ...
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1answer
103 views

What are the following shapes in 3-space?

I have these 3 equations. I tried to use wolfram alpha to graph in 3d, but did't succeed. 1) $x^2 + 2y^2 - 6x + 4y + 7 = 0$ 2) $z^2 - 4z - 6x = 2$ 3) $z = -y + 2$ I think that: 1) is a cylinder 2) ...
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1answer
479 views

Closed-form for eigenvectors of rotation matrix

For matrices that are elements of $SO(3)$ is there a formula for the eigenvectors corresponding to the eigenvalue $1$ in terms of the entries of the matrix?
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1answer
210 views

Implicit equation of an arch in 3D

I have three points: A(85, 85, 0), B(-85, -85, 0) and C(0, 0, 30). I must find the equation of the arch that starts from A, finishes in B and goes through C. Could you help me? I found something ...
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1answer
759 views

3D intersection point between circle and triangle

Given a 3D triangle with vertices $(v0, v1, v2)$ and a 3D circle of radius $r$, centered at $c$, and lying in the plane perpendicular to $axis$, how can I test for intersection points between them? ...
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3answers
140 views

What are some books that I should read on 3D mathematics?

I'm a first-grade highschool student who has been making games in 2D most of the time, but I started working on a 3D project for a change. I'm using a high-level engine that abstracts most of the math ...
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1answer
463 views

Is a 3D Mandelbrot-esque fractal analogue possible?

I understand that (unlike complex numbers) there's no consistent 3 dimensional number system (even 4D loses some nice properties). Regardless, I'm wondering if there might be a 'trick' to create a 3D ...
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1answer
490 views

Find point in 3D space based on start point, three angles and a distance (need example)

I know this has been asked before but the answer wasn't very helpful, sorry. I need an example and to see each step of the equation being solved. Let's say we have 45 degree angles to each axis and ...
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2answers
1k views

calculate field of view from focal length

I am trying to calculate the field of view of a camera from a given focal length and film width. I am using the following equation to do this. FOV = math.degrees(2 * math.atan(filmWidth / (2 * ...
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1answer
1k views

Prove that curve lies on a cone?

I have a curve given by this equation: $$c(t) = (t\cos t,t \sin t,t)$$ I need to prove that this curve lies on a cone, and draw that cone and curve in Sage. I've read somewhere that I could prove it ...
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1answer
111 views

Is there a typo in Calculus:Early Transcedentals?

I just finished doing my homework on Local Linear Approximations in 3-space (Ch.13.4). In one of the problems the answer I got is different from the answer key. Problem 39. We have a function ...
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1answer
199 views

Equation of a parabola-shaped toroidal tube with circular cross-sections

I need an implicit function that plots the surface that I am showing you in the picture. Everything you need is shown there. The surface is a tube in the shape of a parabola. The radius of its ...
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2answers
1k views

How to calculate distance between point and object in 3d space

I have object in 3d space created from points $P_i(x, y, z)$ from which I can create triangles, and I need to calulate distance from point X to this object. I try to take 3 points from smallest ...
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0answers
107 views

Analytic caustics for 3D objects

Is it possible to efficiently calculate caustics for a given 3D object, like a torus, or a cube? To be more precise: let's assume that we have a 3d torus, resting on a 2d plane and a single light ...
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1answer
720 views

Finding the distance between the centre of an arbitrarily rotated cylinder and a point on that cylinder

this is a bit more complicated than the post title suggests because I was running out of words. I suppose the full title would be: "Finding the distance between the centre of an arbitrarily rotated ...
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1answer
84 views

Periodical reflection conditions in a sphere.

A perfect mirror covered the inside surface of a sphere (assumption: there is no any loss during reflection and reflections continue endless) and there is a very small laser on point $A$ in the ...
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3answers
1k views

3-D equation of a circle

I came across a sum but could not solve it as i dont know the 3d equations of a circle : The sum is If $A(3,-2,2)$ and $B(2,9,5)$ are the end points of a diameter of a circle,then the third pt that ...
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1answer
2k views

Icosahedron coordinates

Wikipedia says (link)that cartesian coordinates of icosahedron are: (0, ±1, ± φ) (±1, ± φ, 0) (± φ, 0, ±1) Where φ = (1 + √5) / 2 is golden ratio ≈ 1.618. I ...
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1answer
417 views

Calculating angle of human joint beyond 180° in 3D

I'm having some trouble calculating the angle of an human joint in 3D using the Microsoft Kinect. Here's an example of the angle of the elbow (using the shoulder and wrist joint): Image of example ...
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1answer
201 views

How to fly a curve from one heading to another using only roll and pitch.

I have 3 perpendicular vectors representing an object in 3d space... Heading Right Up ...and I would like to be able to 'fly' this object so that it ends up at a ...
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1answer
445 views

Determining angle of tilt from length of axes?

When taking a picture of a cross, if the center of the cross is known, is there any way to determine the angle at which the picture was taken based on the number of points on the y axis above and ...