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
18 views

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
27 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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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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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
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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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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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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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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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
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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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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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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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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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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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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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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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
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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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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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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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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2answers
44 views

calculate the volume

There is a triangular prism with infinite height. It has three edges parallel to z-axis, each passing through points $(0, 0, 0)$, $(3, 0, 0)$ and $(2, 1, 0)$ respectively. Calculate the volume within ...
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1answer
12 views

How would you find the Cartesian Equation that fits the following requirements?

The Cartesian equation must pass through the point $(3,-1,2)$ and must be perpendicular to the LOI of the planes $3x-2y+1=0$ and $3x+4z-5=0$ Vectors was never really my strong suit, if anyone could ...
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1answer
53 views

How to shift an object to rest on the xy-plane?

For example, I have a cube, which exists somewhere in 3-space, that is composed of edge vectors and vertex points. How can I shift these values so that a face of the cube rests on the xy-plane? I ...
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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
47 views

How can i represent 3D space using 4x4 matrix?

I want to represent 3D space using 4x4 matrix as we represent 2D plane using following form. $$ \begin{bmatrix} cos\theta & sin\theta & 0 \\ -sin\theta &cos\theta ...
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0answers
56 views

Visualising 3rd degree equations

I know that general second degree curve, i.e. $ax^2 + by^2 + 2hxy + 2gx + 2fy + c=0$ gives us the equation of different cross sections of a cone. Similarly, what does a third degree* curve actually ...
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3answers
48 views

Equation of a … 3D object???

(Stupid question...) Well we can represent a point as something like $P(a,b,c)$ We can represent a line as $\dfrac{x-a}{p}=\dfrac{x-b}{q}=\dfrac{x-c}{r}$ We can also represent a plane as ...
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4answers
32 views

Equation of a line that goes through $A(-3,-7,-5)$ and $B(2,3,0)$ and find $C(x, -1, z)$ on the same line

Problem: Find the equation of a line that passes through $A(-3,-7,-5)$ and $B(2,3,0)$ and find $C(x, -1, z)$ on the same line. I have completely forgotten how to solve this and I've been reading ...
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1answer
32 views

In $\Bbb R^3$, is there a general principle governing these “visual” angles?

I believe most of you have drawn the xyz coordinate system hundreds of times and so have I. You may have drawn it like these, on various occasions: (the reverse directions of the axis are not shown.) ...
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1answer
22 views

How to work out the angle of a line passing through a plane

I have a triangular plane composed of three points. From this it it easy to deduce that the plane is in fact composed of two vectors which must touch at some point. because all of this is relative, ...
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1answer
31 views

The area of surface obtained by rotating a rectifiable curve

Let $\Gamma :X=\gamma(t),a\leq t\leq b$ be a rectifiable parameterized curve in the $(x,z)$-plane of $R^3$, which means $\gamma:[a,b]\to R^3$ is a $C^1$-mapping with $\gamma(t)=(x(t),0,z(t))^T$ and ...
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2answers
46 views

Find the curve, given that $r'(t) = Cr(t)$

I need to find the curve, given that $r'(t) = Cr(t)$ (where $C$ is a constant), for all real $t$ and $r(0)=i+2j+3k$. To start, I know that the equation I will need is the $$K=\frac{||r'(t) \times ...
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0answers
19 views

Euler Angle Transformation from righthanded to lefthanded cartesian coordinate system

I have a righthanded and a lefthanded cartesian coordinate system defined as follows: I have Euler angles (x, y, z) defined in the righthanded system and want to transform them to the lefthanded ...
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2answers
25 views

How many unique vertices in octahedron based sphere approximation

Using a triangular facet approximation of a sphere based on Sphere Generation by Paul Bourke. We take an octahedron and bisect the edges of its facets to form 4 triangles from each triangle. ...
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3answers
53 views

Breaking down the equation of a plane

Could someone explain the individual parts of a plane equation? For example: $3x + y + z = 7$ When I see this I can't imagine what it's supposed to look like.
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0answers
27 views

Taylor expansion need help understanding.

I am at the moment reading a paper (SURF) and trying to understand what is happening here and how the things works as it does.... a non maximum supression is performed on the scale space ...
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1answer
23 views

Will the normal of a normal of an edge give me back the edge?

I have an edge in 3d, which is basically a 3d vector. So, by calculating the normal of the edge, I will have a vector perpendicular to the edge. Therefore, does that mean, if I calculate the normal of ...
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0answers
6 views

Question regarding Calibration while using Phase Measuring Profilometry (PMP)

We are using PMP to create the 3d model of a real world object in a summer project. However, to actually use PMP we need to relate the camera and the projector parameters and coordinates. To ...
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0answers
9 views

Dinamically generate Goldberg polyhedra G(m,n)

In these pages the autor provided a lot of info about some Goldberg polyhedra (http://en.wikipedia.org/wiki/Goldberg_polyhedron): http://dmccooey.com/polyhedra/DualGeodesicIcosahedra.html ...
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0answers
28 views

Compute volume of the tetrahedron from circumsphere test

I'm working on a computational geometry algorithm. In every iteration I solve the matrix below, where (a,b,c,d) are the vertices of a tetrahedron, and e is an arbitrary point. Solving the determinant ...
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77 views

Is it 3-D Catalan numbers?

I am studying Catalan numbers recently but I think that how about 3-D Catalan? So that I imagine following situation ; A man travel through the path-way parallel to $ x, y, z $ axis from O ...