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
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Get the Equation of a Plane from a Vertex and 2 Angles?

What is the simplest way to algebraically get the equation of a Plane (ax + by + cz = d), if you only have 1 point on the plane, and 2 angles (horizontal and vertical) which define the direction the ...
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2answers
179 views

Calculate distance after rotation?

I'll start off by saying that I suck at math. I'm trying to calculate the distance between a circle and the center of the screen after rotating an image that contains that circle by $45^\circ$ in ...
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0answers
143 views

are oblique projections one specific subdivision of trimetric projections?

So I've reaserched a while and come with this broad definitions a projection is the representation of a 3D object in 2D by the use of "imaginary proyectors"(cameras of some sort). it has 2 branches, ...
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1answer
403 views

Intersection of a line segment and a paraboloid in 3D

Suppose I have a line segment $L$ in 3D: $$x=a_1(1-t)+b_1t$$ $$y=a_2(1-t)+b_2t$$ $$z=(a_1^2+a_2^2-k_1^2)(1-t)+(b_1^2+b_2^2-k_2^2)t$$ Because $L$ is line segment then $0\leq t\leq 1$. And defining ...
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1answer
365 views

Find normal vector of circle in 3D space given circle size and a single perspective

I don't really know what to search up to answer my question. I tried such things as "ellipse matching" and "3d circle orientation" (and others) but I can't really find much. But anyways... I have ...
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1answer
191 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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1answer
30 views

Find angles between sides of triangle and coordinate planes ($xy,yz,zx$ planes) using three 3d vectors .

Given the following, three vectors: \begin{align*} \vec{a}& = 3i−2j+5k, \\ \vec{b}& =i−6j+6k, \\ \vec{c}& =2i+3j−k, \\ \end{align*} find the angles between sides of triangle and ...
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2answers
1k views

How can I determine the radius of a dodecahedron?

I am making a dodecahedron that needs to fit inside of a sphere. The sphere has a diameter of 56mm. What is largest possible measurement of one segment of a pentagon side of a dodecahedron that would ...
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2answers
26 views

Get the camera transformation matrix (Camera pose, not view matrix)

Let's say that I have an object and a camera (its representation) in a 3D world coordinate system. I have the camera pose to see the object (rotation matrix and translation (eye position)). If I apply ...
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1answer
19 views

Curvature of a 3D trajectory for which I know data points

In order to simulate an airplane model, I need to change its orientation knowing the curvature of its trajectory. The simulator gives me the plane position, so in order to perform my orientation ...
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2answers
27 views

Find 3D distance between two parallel lines in simple way

Is there a simple way to get 3D distance between two parallel lines given end points of each line?
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0answers
11 views

Get range of 3D object given lowest and highest point

How do you get 3D range of object (highlighted in red below) given its lowest (PL) and highest (PH) (x,y,z) coordinates and the dimensions and orientation of object?
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1answer
299 views

Finding the coordinates of a point on a line that produces the shortest distance to another point in 3 dimensions.

I have a question with two parts and it looks like the following: a) Determine the distance from point $A(-2, 1, 1)$ to the line with the equation $\vec{r} = (3, 0, -1) + t(1, 1, 2)$, $t\in \Bbb R$ ...
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2answers
2k views

distance between parametric line and a point $(4,3,s)$

I've tried solving this problem every way I know how and I just can't get it. I've looked at similar problems of this type, and I still cannot get an answer that seems right. Parametric Equations: ...
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0answers
9 views

Calculate camera view and projection matricies from projected points

I’m stuck on a project for a client.. I need to find the answer to this to proceed: Given (n) coordinates in 3D space and (n) corresponding coordinates in 2D space as projected onto a camera’s image ...
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3answers
44 views

possible polyhedra from euler's formula

I'm not very clear with the euler's formula, and I couldn't find it anywhere. I'm sorry if it is a double post. F + V - E = 2 Is the euler's formula. If the equation balances, is it polyhedra all ...
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1answer
8 views

Point within a Cube in 3D environment

I have a cube in 3D space with 8 corner points with their X,Y,Z Coordinates. I know how to test if any given point lies inside a cube by Comparing their coordinates to be greater or smaller than the ...
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0answers
22 views

transofrmations (a,b,c) to (x,y,z)

I'm not 100% sure linear algebra will crunch this problem, but hopefully so. This may just be a case of matrices, which would be good cause I like those. Imagine we have a robot with a camera ...
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1answer
288 views

number of planes possible such that it is equidistant from 4 non coplanar points

If there are for non coplanar points find the number of planes such that all four of them are equidistant from the plane . Sorry one of those problems where dont know what to do . How should i do this ...
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0answers
17 views

finding the intersection points of three semispheres

I'm currently playing with a project where the math is far over my head. I know enough to visualize it, but not enough to solve it from the numbers. I'm setting up three listening posts on the tips ...
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0answers
19 views

Cartesian/Parametric 3d equation of a cheese twist?

Hi I'm looking for the equation of a cheese twist in 3d (either parametric or cartesian)... Can be multiple planes but was wondering if anyone had any idea to execute something like this? Thanks e.g. ...
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2answers
57 views

Rotate a unit sphere such as to align it two orthogonal unit vectors

I have two orthogonal vectors $a$, $b$, which lie on a unit sphere (i.e. unit vectors). I want to apply one or more rotations to the sphere such that $a$ is transformed to $c$, and $b$ is transformed ...
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2answers
53 views

Find perimeter and angle of triangle using three 3d vectors .

Given the following, three vectors: $$\vec{a} = 3\mathrm{i} - 2\mathrm{j} + 5\mathrm{k}\\\vec{b} = \mathrm{i} - 6\mathrm{j} + 6\mathrm{k}\\\vec{c} = 2\mathrm{i} + 3\mathrm{j} - \mathrm{k},\\$$ find ...
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1answer
11 views

Finding the best direction for a bird escape from a radiation (function of 3 parametres)

I have this question. My bird is is in this point: (1,1,3) in 3D, and the source of the radiation is in that point too. What is the direction for her to fly from that point, if it wants to minimize ...
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1answer
22 views

Number of components needed for 3D rotation

Using Euler angles, a 3D rotation can be expressed using 3 real numbers. Using quaternions, 4 are needed and using rotation matrices 9. Is it possible to express a 3D rotation using less than 3 real ...
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0answers
19 views

Camera calibration: how does checkerboard size/numbers/placement affect accuracy

I am trying to calibrate a camera using a checkerboard by the well known Zhang's method followed by bundle adjustment, which is available in both Matlab and OpenCV. There are a lot of empirical ...
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1answer
12 views

What unit is the first derivative of a quadratic Bézier curve expressed in?

I'm using quadratic Bézier curves to determine the velocity vector at the endpoints of a path - I know only discrete points, not the velocity in those points. The velocity vector is supposed to be the ...
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1answer
470 views

Jacobian of exponential mapping in SO3/SE3

Following this post Jacobian matrix of the Rodrigues' formula (exponential map) What if I really need the Jacobian of the exponential mapping function in $\omega \neq 0$? Basically, I want to ...
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1answer
19 views

Points on two skew lines closest to one another

Given two skew lines defined by 2 points lying on them as $(\vec{x}_1,\vec{x}_2)$ and $(\vec{x}_3,\vec{x}_4)$. What are the vectors for the two points on the corrwsponding lines, distance between ...
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0answers
12 views

Representation of a cone in 3D

I need to find the representation of a cone in the 3D space with the following criteria: It's tip is located at the origin. It opens in the positive direction of the axis (it’s one-sided). The ...
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1answer
39 views

Compute ratio of a rectangle seen from an unknown perspective

TL;DR: Given 4 points on a two dimentional plane, representing a reclangle seen from an unknown perspective, can we deduce the width / height ratio of the rectangle ? Details: From a picture, and ...
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1answer
31 views

get third point from an arc constructed by Start point, end point and bulge

it's been a long time since I have done some basic geometry, but I need to construct an arc from three points: start point, end point, and one other point located on the arc, preferrably the point on ...
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0answers
36 views

how do you find the intersecting points of three $3d$ cones with origin and angle

I'm working on a project and I'm a developer. the math is a bit, well, way beyond me. I can visualize things enough to see that they should work, but that's as far as my brain can take me on this one. ...
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0answers
14 views

Finding intersections of tori/toruses

I am looking for intersections of three tori. Is this possible? If so, how? To put things in perspective: I am looking for the coordinates of point P in space, and I have a triangle on the 'ground'. ...
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2answers
97 views

Determining complexity of a 3D shape

This is my first foray outside of stack-overflow, so I hope this is an acceptable forum for this question. I want to calculate a 'complexity' index based of 3D models. Currently I'm calculating the ...
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1answer
32 views

Find corners of a square in a plane in 3d space

I am given two angles (similar to theta and phi in spherical coordinates) from which I can calculate a normal vector to a plane in 3d space. I am also given the center point of the square and the area ...
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1answer
781 views

Determining which side of a 3D cube is facing the viewer

Me and a friend are trying to render a rotating cube on a 2D plane(the screen) using java. Here's the problem The cube has 6 sides, each with a specific normal vector of the form $(0, 0, 1)$, $(0, ...
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1answer
16 views

Interpolate between 3D plane and 3D hemisphere

I have a simple 3D plane whose points (different $x, y$ values, but all $z = 0$) need to be mapped to 3D Cartesian coordinates in order to form a hemisphere. However, I also would like to be able to ...
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2answers
2k views

How to calculate volume of 3d convex hull?

Convex hull is defined by a set of planes (point on plane, plane normal). I also know the plane intersections points which form polygons on each face. How to calculate volume of convex hull?
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2answers
425 views

How to divide a $3$ D-sphere into “equivalent” parts?

My goal is to put $n$ points on a sphere in $\mathbb{R}^3$ to divide it in $n$ parts, so that their disposition would be as "equivalent" as possible. I don't exactly know what "equivalent" ...
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1answer
2k views

Distance from a point to circle's closest point

So let's assume I have a point $P$ in $3D$ space $(x_0, y_0, z_0)$. And I have a circle $C$ that is centered at $(x_1, y_1, z_1)$ with a radius $r$. I need to find the distance from $P$ to the nearest ...
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1answer
19 views

Question about 3D vectors and their line equations.

Let ${a} = \begin{pmatrix} 5 \\ -3 \\ -4 \end{pmatrix} \quad \text{and} \quad {b} = \begin{pmatrix} -11 \\ 1 \\ 28 \end{pmatrix}.$ There exist vectors ${p}$ and ${d}$ such that the line containing ...
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0answers
22 views

Shared Volume of Overlapping 3D Cubes/Rectangles

Good afternoon, I have been looking for an approach to figure out the volume where two cubes/rectangles overlap, meaning, I know when they do, I just don't know the coordinates of the volume in which ...
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1answer
478 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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2answers
1k views

calculating perpendicular and angular distance between line segments in 3d

I originally posted this over at stackoverflow and they suggested asking it over here. link to original: ...
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2answers
1k views

Combining Two 3D Rotations

Every rotation in 3D space can be defined by a rotation axis and an angle. Now let's say we have two rotations $R_1 (\text{(axis)}_1, \text{(angle)}_1)$, $R_2 (\text{(axis)}_2, \text{(angle)}_2)$. I ...
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2answers
9k views

How to find shortest distance between two skew lines in 3D?

If given 2 lines $\alpha$ and $\beta$, that are created by 2 points: A and B 2 plane intersection I want to find shortest distance between them. $$\left\{\begin{array}{c} P_1=x_1X+y_1Y+z_1Z+C=0 ...
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2answers
19 views

How to check if a point is in the direction of the normal of a plane?

I have a plane, defined by a normal vector $n$ and a point $p$. I also have a point $a = (x, y, z)$. Based on this information, how do I know if the point $a$ exists somewhere past the plane in the ...
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0answers
55 views

Calculating object position in 3D space

I'm looking for an algorithm to calculate the position of point P in space using a triangular(/rectangular) plane on the 'ground'. The position between the points ABC of the triangle on the ground are ...
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1answer
315 views

Ellipsoid intersection

Let $E$ be an ellipsoid centered at $p = (x,y,z) \in \mathbb{R}^3$ and let $T:\mathbb{R}^3 \to \mathbb{R}^3 $ be a linear transformation which transforms $E$ to a unit sphere. Let $R$ be the ray $p_0 ...