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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2answers
11 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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0answers
18 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
19 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
5 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
7 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
30 views

Understanding the lookAt function

I am trying to understand from here and here how to work with the concepts behind the lookAt function. I have made this animation to illustrate my question, where I want to set the orientation for ...
2
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0answers
20 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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2answers
40 views

What result multiplying 2 3D-vectors? [closed]

I understood that multiplying two vectors by cross multiplication(!) results in a third vector which is orthogonal to the two first. What does multiplying 2 3D-vectors give us as a result? What ...
3
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0answers
63 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
40 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 ...
1
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3answers
49 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
49 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
55 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 ...
2
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1answer
58 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 ...
1
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1answer
38 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
34 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
17 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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0answers
28 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
47 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 ...
0
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1answer
27 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 = ...
0
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0answers
16 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 ...
0
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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
21 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 ...
1
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2answers
24 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 ...
5
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0answers
22 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
11 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 ...
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1answer
16 views

Finding end point of a segment, given start point and inclination

Consider a line segment whose start coordinates $(x,y,z)$ are known, and whose inclination $(a_1,b_1,c_1)$ in all $3$ planes is also known. The length of the line segment is known too. How do we find ...
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0answers
11 views

Angle between two lines formed by intersection of two planes with X = 0, Y = 0 and Z = 0 planes

I am new to linear algebra and have been struggling with a solution for this since long. I work on MATLAB. I have a set of points (as in Points3D.mat attached here). I find the equation of best fit ...
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0answers
43 views

An example of 4D Hypersurface in 3D

Number of combinations of 4 dimensions choosing 3 at a time is 4. Someone please give a description of a most elementary 4 Dimensional Hyper surface which has its four 3D intersections with ...
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3answers
49 views

finding a third 3d point in a series

Given two three dimensional points. find the z coordinate of a third point that has two known coordinates. I'm not entirely sure how to solve this system. I'll be implementing this into an algorithm ...
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1answer
27 views

Is it possible to create a parabola by intersecting a hyperboloid of one sheet and a plane?

By which I mean, is there anyway that the intersetion of a plane and a hyperboloid of one sheet will be a parabola? I know that intersecting a plane and a cone so that the plane is parallel to the ...
4
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2answers
42 views

How to calculate line-line distance when cross product of directions is 0?

I have the lines $$\frac{x-1}{2} = 1-y = \frac{z-2}{3} \tag{1}$$ and $$\frac{x+1}{4} = \frac{4-y}{2} = \frac{z+1}{6} \tag{2}$$ I want to compute the distance between them. I started by putting ...
2
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0answers
22 views

Calculate vector of an object aligned to another object in a 3D envorionment

I have an object (100x100x5) with given coordinates and angles. Now I want to place another object aligned to the left/right side of the "original" object. On the X-Axis I need to substract/add 100, ...
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3answers
71 views

What does the 2nd degree derivative of a cubic Bezier curve actually represent?

I have a $3D$ Bezier curve. Each co-ordinate along its path is defined by the equation: $$ f(t) = t^3 \bigl(a_2+3(c_1-c_2)-a_1\bigr) + 3t^2 (a_1-2c_1+c_2) + 3t(c_1-a_1) + a_1 $$ where $a_1, a_2$ are ...
1
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0answers
19 views

How to compute the best fitting frustum for a set of points?

I am struggling with a problem that I am sure is well known, but I could not find any answer using google or searching on MathOverflow. I have a set of 3D points (x,y,z) and a camera reference frame ...
0
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1answer
24 views

what is the difference between an elliptical and circular paraboloid? (3D)

My textbook uses the terms interchangably, and they look the same in graphs, so I was wondering if there a difference between the two? Thanks!
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2answers
29 views

How to calculate the center of mass for a cloud of 3D spheres?

Given the spheres in 3D space: center(xi,yi,zi), radius and density and the info is stored in an array sphere_data[n][5]: // Sphere_ID x y z radius density 1 x1 y1 z1 rad1 ...
0
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0answers
47 views

Finding position of point (in 3D space ) which are at x,y offset from corner of a rectangle in 3D world

So I am writing a 3D graphic software. And I am stuck at mathematical problem. Mathematically speaking: There's a rectangle (plane) of finite size in 3D space. It can be of any orientation and ...
2
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1answer
66 views

How can we prove that a three legged chair will never be wobbly?

I am taking the geometry approach. We know from intuition that more than three legs on a chair will make it unstable if any of the legs have a different length than the others. So by "wobble" I mean ...
1
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1answer
32 views

Expression of rotation matrix from two vectors

What is the matrix expression of the rotation matrix in 3D which turns a vector $\vec{a}$ into a vector $\vec{b}$, with both vectors given by their coordinates? ($\vec{a} = (a_x, a_y, a_z)$ and ...
0
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1answer
36 views

Determining if a point is inside an infinite 3d elliptical tilted cone

I have an infinite 3d elliptical, tilted cone that is defined by a vertex point P(x,y,z) and by 4 angles: the first pair of angles represent the spatial orientation of the cone: θ is the polar angle ...
1
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2answers
129 views

Plane intersecting all the lines

This might sound a bit stupid or ill thought, but I am having trouble visualizing it and proving it. Given a finite set $L$ of straight lines in $\mathbb{R^3}$ is it always possible to find a plane ...
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0answers
13 views

Calculate the plane angle from 2D plane

I am analysing a squared plane from a perfect cube. This plane is distorted by the perspective view of a camera. I would like to know ask please, some approaches of how could I get to know the ...
0
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1answer
23 views

What does this volume represent?

I have been trying to draw this out for an hour now and cannot visualize it. $x$ is between $0$ and $1$, $y$ is between $0$ and $x$, and $z$ is between $x^{2}+y^{2}$. The $z$ line is just a ...
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0answers
47 views

How to draw regular tetrahedron from center?

How to calculate all four points of regular tetrahedron if you have x,y and z for center point and x, y and z axis rotation and size of tetrahedron? I want to write this in java script and this is ...
0
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0answers
21 views

How to construct a surface with a closed curve?

in 3-dimension, suppose that there is a smooth closed curve $C$. Can I say that there is a smooth simply connected(no holes) surface whose boundary is $C$? and is it unique?(I guess not) like ...
0
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1answer
20 views

Square surface with four fixed points

I'm looking for a function of two variables, $f(x, y)$, that satisfies the following constraints: $f(0, 0) = z_1$ $f(0, 1) = z_2$ $f(1, 0) = z_3$ $f(1, 1) = z_4$ and within the unit square, it ...
0
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2answers
43 views

The point A (4, 3, c) is equidistant from the planes P1 and P2. Calculate the two possible values of c

The point $A (4, 3, c)$ is equidistant from the planes $P_1$ and $P_2$. Calculate the two possible values of $c$. Plane $P_1$ has equation $r\cdot (2,-2,1)=1$ Plane $P_2$ has equation $r\cdot ...
4
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2answers
91 views

How do I find the Intersection of two 3D triangles?

I've got a rather complicated geometry problem that I'm trying to solve - how to find the intersection between two triangles in 3D space. I've looked around at other questions and answers on this site ...
0
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1answer
35 views

Three-Dimensional Metrics as Deformations of a Constant Curvature Metric?

I read the following paper Three-Dimensional Metrics as Deformations of a Constant Curvature Metric and discovered the following result: I have three questions: (1) Is $h$ also a conformally flat ...