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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4
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2answers
115 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 ...
0
votes
2answers
63 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 ...
0
votes
1answer
17 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 ...
0
votes
1answer
124 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 ...
0
votes
1answer
203 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 ...
5
votes
0answers
68 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 ...
3
votes
3answers
119 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 ...
2
votes
4answers
46 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 ...
2
votes
1answer
40 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.) ...
0
votes
1answer
28 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, ...
0
votes
1answer
41 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 ...
1
vote
2answers
50 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 ...
0
votes
0answers
82 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 ...
1
vote
2answers
63 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. ...
1
vote
3answers
59 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.
2
votes
0answers
34 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 ...
0
votes
1answer
46 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 ...
0
votes
0answers
12 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 ...
2
votes
0answers
27 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 ...
2
votes
0answers
71 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 ...
3
votes
0answers
106 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 ...
1
vote
2answers
60 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
vote
3answers
59 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 ...
1
vote
2answers
58 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 ...
0
votes
0answers
104 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
votes
1answer
121 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
vote
1answer
154 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 ...
0
votes
1answer
54 views

Maximum angle between two vectors obtained by cyclic permutations of coordinates [closed]

If $a, b, c$ are direction cosines of a line and $\vec{A} = a\hat{i} + b\hat{j} + c\hat{k}$, $\vec{B} = b\hat{i} + c\hat{j} + a\hat{k}$, then find the maximum angle $\theta$ (in degrees) between ...
1
vote
1answer
74 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 ...
-1
votes
1answer
30 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 $z$?
0
votes
0answers
44 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 ...
6
votes
1answer
80 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
votes
1answer
369 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
votes
0answers
26 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
votes
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: ...
1
vote
0answers
98 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
vote
2answers
138 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
votes
0answers
55 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 ...
0
votes
1answer
53 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 ...
0
votes
0answers
106 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 ...
1
vote
3answers
96 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 ...
0
votes
1answer
39 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
votes
2answers
100 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
votes
0answers
25 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, ...
1
vote
3answers
437 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
vote
0answers
51 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
votes
1answer
992 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!
1
vote
2answers
50 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
votes
0answers
192 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
votes
1answer
133 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 ...