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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1answer
596 views

Calculating an average plane from a series of points using Numpy [closed]

Given N, 3D position vectors, I want to find the best-fit plane of those vectors. I found a suggested answer here that said: Calculate the average of the points (easy) Calculate the Covariance ...
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0answers
78 views

Modeling with a Bivariate Gaussian Distribution

In an earlier question I inquired about contour lines reflecting probability values in a Bivariate Gaussian Distribution. I have spent some time thinking and playing around with a Mathematica ...
0
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1answer
130 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
2k 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, ...
7
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2answers
4k 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
164 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, ...
4
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1answer
454 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
290 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
119 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
305 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 ...
7
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1answer
602 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 ...
4
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2answers
572 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
313 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
89 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
332 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
158 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
478 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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1answer
102 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 ...
5
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1answer
334 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
397 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
954 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
417 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
104 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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2answers
790 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
67 views
+50

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
403 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 ...
3
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1answer
72 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
597 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
635 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 ...
2
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1answer
233 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
159 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
263 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 ...
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2answers
474 views

“Normalizing” Points on a Sphere

I have a set of points on a unit sphere representing different orientations: Now I need to apply rotation(s) such that the points will lay on the horizon as tightly as possible: The ideal ...
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2answers
82 views

Normal from multiple vectors

I have a several 3D vectors $X_{i}$ which lay approximately in a plane. Now I need to find a single vector, which is normal (as much as possible) to all of them. For two vectors, I can use a cross ...
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2answers
194 views

Need to define an integral expression to find the area of intersection of a Plane and a Cone.

How can the integral expression be defined to find Area (S) on $x+y+z=1$ and bordered with intersection of the cone ($x^2+y^2-z^2=0$) and the plane ($x+y+z=1$) ?
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1answer
2k views

Finding an equation of a sphere for a specific plane

I am not sure how to proceed with this question from Stewart's SV Calculus text: Find equations of the sphere's with center $(2, -3, 6)$ that touch (a) the $xy$-plane, (b) the $yz$-plane, (c) ...
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3answers
434 views

What is the tangent plane equation on the 3 spheres?

3 spheres are on $z=0$ plane and touch each other as shown in the picture. Coordinates of their centers are $O_1=(0,0,5),O_2=(0,y_2,3),O_3=(x_3,y_3,2)$. What is the tangent plane equation on 3 ...
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3answers
13k views

how to calculate area of 3D triangle?

I have coordinates of 3d triangle and I need to calculate its area. I know how to do it in 2D, but don't know how to calculate area in 3d. I have developed data as follows. ...
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1answer
124 views

Find P points inside ABCD tetrahedron so that volume of ABCP = volume of ABDP

Find all $P$ points inside $ABCD$ tetrahedron, so that $V_{ABCP} = V_{ABDP}$ Thanks in advance for any help.
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1answer
153 views

Should/do parallel lines curve when rendered with perspective?

Simple perspective calculations used in rendering 3D points onto a 2D screen take the form of dividing the camera-relative coordinates by distance from camera and multiplying by a field-of-view ...
0
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1answer
146 views

Calculate equivalent (X,Y) given (X,Y,Z)

I'm working on generating a 3D-looking application (in 2D) and am having difficulty generating my graphing points equally. I can only graph in 2D, but want to have a 3D look to it (similar to a ...
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3answers
1k views

Quaternions and spatial translations

From my understanding, in spatial applications (3D rendering, games and similar applications) quaternions can only be used to describe rotations/orientations and not translations (like a ...
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0answers
109 views

polygon inside a polygon

i have several point patches lie on different planar faces. then, I obtained enclosing polygons to represent points so that i have several planar polygons (for example A,B,C,D). when i examine the ...
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0answers
320 views

differentiation of polygons, having cross borders

I have point data set and I segmented the data into different planar objects. after that, using contouring (convex hull), I obtained the boundary points. Please assume all points relevant to one ...
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0answers
84 views

Can 2 parallel lines be discriminated as 'away', 'beside' with respect to 3rd parallel line?

I have nearly parallel several 3D line segments. some line segments locate (blue line) beside to a spefic line segment (black line) and some other (red line) locate away from that line segment. i want ...
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2answers
708 views

How are 3D coordinates transformed to 2D coordinates that can be displayed on the screen? What is the formula for this?

The title asks it all, and could someone please also explain the formula as well? Thanks.
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1answer
298 views

Finding radius r of the overlappable sphere(s) in 3D image

My current problem: I have an input 3D binary image (a 3D matrix that has only 0 and 1) that consists of random numbers of sphere with radius r. We do not know how many spheres are there in the ...
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1answer
502 views

Find 3D rotation vector and angle to transform a rectangle into a given quadrilateral

I have a given rectangle that I need to transform into a given quadrilateral shape that resulted from a rotation and translation in 3D space, and subsequent projection. ...
0
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1answer
151 views

Chain Rule and Homogenous Coordinates

I have a vector $\tilde{p} = (x,y,z)$ (homogenous coordinates). The corresponding non-homogenous vector is $p = (x/z, y/z)$. Now the $\tilde{p}$ is a result of some linear transform $R(\theta)$ of ...
3
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2answers
660 views

Extend angle between two 3D vectors to x-y plane.

I would like to know how I can extend the angle between two vectors in 3D space to the x-y plane. So, there are two vectors in 3D space, and the angle between them is found using the definition of ...