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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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
69 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
40 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
15 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
36 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
33 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
25 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
27 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
22 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
99 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
47 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
13 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
54 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
62 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
59 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
59 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
52 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
34 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
23 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
33 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
28 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
31 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
28 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
25 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
8 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
16 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
36 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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0answers
80 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 ...
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2answers
45 views

Discretization of Unit Vector in 3D

I cant think of a thing that I think is supposed to be easy... =/ Im glad if you could help me. Im working with a regular discretization of a 3d euclidean space. Cubic cells. Then, after a ...
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3answers
51 views

Perpendicular vectors in 3d

Suppose a vector $v$ in $\mathbb{R}^3 $ How can I find two arbitrary unit vectors $u$ and $u^*$, that are perpendicular to each other and $v$ ? There are infinitely many solutions, but I cannot ...
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2answers
53 views

Tetrahedra from it's inscribed sphere

I'm facing a geometrical problem: Given a sphere S, I want to calculate the vertices of the tetrahedra T whose inscribed sphere is S. In other words I want to calculate a tetrahedra from it's ...
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0answers
73 views

3D surface intersections

I tried to look at 3D Hypersurface intersections of 4D this way based on four Mathematica (circular) trigonometric parametrization combination selections. No hyperbolic functions are directly ...
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1answer
65 views

Is there a nice meaning to the geometric triple product?

Using geometric algebra, I can easily find the geometric tripleproduct of three vectors $a,b,c \in \mathbb{R}^3$ to be $$abc = a \left(b \cdot c \right) - b \left( c \cdot a \right) + c \left( a ...
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1answer
57 views

3D rotation of an object with respect to another object's rotation

I am writing a python code to translate and rotate an object with respect to another object. Please take a look at the picture bellow: The smiley face and the arrow have initial poses (position ...
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1answer
44 views

Approximate model of a convex/concave surface

I have a set of measurements in 3d that yields a concave surface of a function $f(x,y)$ that I don't know its expression. I am thinking to approximate the function to a model where any point from the ...
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1answer
22 views

Find $y$-coordinate of point on three-dimensional rectangle.

Given a quadrilateral in $3$-dimensional space and the coordinates of each of its vertices, can I find the $y$ of any point on this quadrilateral given this point's $x$ and $z$?
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32 views

Question on 3-D Geometry

Consider the planes passing through the line of intersection of the planes 2x+y-z=5 and x+2y+z=6 and equally inclined to both planes. If the equation of the equally inclined plane is x+ay+mz=n , then ...
5
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1answer
61 views

Perfectly Round Sphere on Perfectly Flat Floor

I know that in practice it may be practically impossible to create the following situation, but suppose I did place a perfectly round ball of radius r (not that I think radius r is relevant) on a ...
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1answer
54 views

3D Vector defined by 3 angles trigonometry components

What I'm looking for is the trigonomery equations to calculate the x, y and z components of a 3D vector. What I mean: The counterpart formulas for a 2D vector defined by 1 angle: $x = ...
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0answers
21 views

Education tool for learning 3D angles

I hope it is not an off-topic. I have started working on 3D frame transformation and transforming a vector such as acceleration or angular velocity from one coordination to earth coordination. My ...
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0answers
27 views

Solving LES containg spherical coordinates

i have a three-dimensional parametric equation of a line, where the directional vector is normalized and converted to spherical coordinates to calculate a angle offset. It looks like this: ...
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0answers
38 views

Calculate point's coordinates relative to rotation in 3D-space

I have a point "A" in 3D-space, let's say in coordinates (2, 3, -1). Then there's a point "B" which position is A + (-1, 2, -1), so now it's ...
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2answers
34 views

How to function fit a plane through a collection with points with minimal square root of error

I'm working on a computer program that has to stabilize a set of points which should all appear on a plane in 3D space. Currently the program does not use the knowledge that all points should appear ...
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0answers
29 views

Does a point quadrilateral form a rect in 3D space?

I have 4 points with x and y coordinate and would like to find out a way to check if given quadrilateral would be a rectangle in 3D space. I tried a bunch of conditions, but there was always and edge ...
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0answers
27 views

Comparing paired objects in 3d space using direction angles.

I have data about paired objects in 3d space, where each object is defined by three components. What I would like to do is compare the orientations of the paired objects and see if one group of those ...