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.
0
votes
2answers
43 views
Books for Geometry processing
Please suggest some basic books on geometry processing.
I want to learn this subject for learning algorithms in 3d mesh generation and graphics.
Please suggest me subjects or areas of mathematics i ...
1
vote
1answer
31 views
3D Circle/ground intersection
This one stumps me: A circle in 3D space given by its center = $(0.15, 0.5, 1.0)$, its radius $=64$ and an orientation vector that points away from the circle's plane $(0.251, -0.796, 0.551)$
How ...
3
votes
2answers
29 views
Rotation of a point in 3d space
I'm trying to rotate a point around a single axis of a 3D system.
Given $P=\begin{pmatrix}
101 \\
102 \\
103
\end{pmatrix}
$,
And the rotation matrix formula for rotation around the X axis only, I ...
1
vote
2answers
109 views
Is the value of $\pi$ in 2d the same in 3d? [closed]
I am starting with my question with the note "Assume no math skills". Given that, all down votes are welcomed. (At the expense of better understanding of course!)
Given my first question: What is ...
2
votes
1answer
56 views
question from hatcher basic 3 manifolds
The question is: why should a homologically trivial embedded sphere in a simply connected (not necessarily compact) 3 manifold M bound a compact 3 manifold embedded in M?
I had this problem reading ...
0
votes
0answers
12 views
Cubic interpolation in arbitrary dimension?
Consider a $N$-dimensional space discretized with a regular cubic grid of $n^N$ cubes, each cube containing the value of a function $f$ in its center. How to correctly interpolate $f(x, y, z)$ using ...
0
votes
1answer
27 views
Intersection between sphere and cylinder
I have a sphere and a cylinder.
I have the center and the radius of each of them.
the sphere:
radius = $r_1$
center = $(x_1,y_1,z_1)$
the cylinder:
radius = $r_2$
height = $h_2$
center = ...
0
votes
1answer
29 views
Get the equation for a plane when we know a point and an intersection between two planes
The point is $P:(1,4,-2)$ and the two planes that the equation intersect is $$\pi_1:2x+2y-z+4=0$$$$\pi_2:3x-y+3z+1=0$$ what is the equation?
7
votes
2answers
106 views
Cross section is a regular hexagon.Is it a cube?
One of the cross sections in a rectangular box is a regular hexagon.Prove that the box is a cube
I tried to prove that certain lengths were equal by showing that certain triangles are congruent but ...
0
votes
1answer
45 views
Rotate a plane along a line in 3d space
I have a plane A in 3D which can be defined either by the scalar plane equation or by its normal n. I want to find a new plane B which is orthogonal to plane A but shares an edge with plane A. I.e. I ...
0
votes
2answers
40 views
Calculate distance from plane to parallel plane in O using vector and normal
I'm trying to figure out what's the best method to get the distance between two planes where i have the normalized vector of the plane and a point in the plane. What I want to do is to create a ...
-1
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0answers
25 views
Imaginary line passing through non-collinear points in R3.
I have come to a problem where n points are provided in 3-Dimensional plane. I need a imaginary line which can be assumed that it is passing through these points.
0
votes
1answer
36 views
Shortest distance between a 3D parametric surface and a point
Right now I'm working on a library for finding the distances between objects in Lua. I've had some trouble finding the distance between a point and a bounded plane. I'm using these parametric ...
0
votes
3answers
53 views
Composition of two axis-angle rotations
Please note that I am not referring to Euler angles of the form (α,β,γ). I am referring to the axis-angle representation, in which a unit vector indicates the direction axis of a rotation and a scalar ...
3
votes
4answers
152 views
What's the best 3D angular co-ordinate system for working with smartfone apps
This is very much an applied maths question. I'm having trouble with Euler angles in the context of smartphone apps. I've been working with Android, but I would guess that the same problem arises ...
0
votes
0answers
31 views
Mymultiple image geometry
I have to work with multiple aerial images. the objective is to reconstruct 3d features.
For a particular object, i want to find the images which are giving good viewing geometry than others. so ...
0
votes
1answer
25 views
Finding point in two parallel lines in 3d?
The line $L_1$ that goes through the point $A(4,3,-2)$ and its parallel to the line $(x=1+3t, y=2-4t, z= 3-t)$, if $P(m,n,-5)$ belongs to $L_1$, determine the values for $m$ and $n$
I really don't ...
1
vote
1answer
45 views
Rotate 3d plane
I have a plane in 3D space that formed from 3 poin $P_1=(x_1, y_1, z_1)$, $P_2=(x_2, y_2, z_2)$, $P_3=(x_3, y_3, z_3)$
I want to rotate and transform this points (equally related plane) into 2D space ...
3
votes
1answer
87 views
Finding intersection of 2 planes without cartesian equations?
The planes $\pi_1$ and $\pi_2$ have vector equations:
$$\pi_1: r=\lambda_1(i+j-k)+\mu_1(2i-j+k)$$
$$\pi_2: r=\lambda_2(i+2j+k)+\mu_2(3i+j-k)$$
$i.$ The line $l$ passes through the point with ...
1
vote
1answer
82 views
Coordinate Transformation on Local coordinate system
I am having a point $P(x,y,z)$ in $3D$ with respect to global coordinate system. I want to create an another Local Coordinate System by picking three points $N1, N2, N3$ in 3D. Now I want to know the ...
1
vote
1answer
35 views
Finding the possible lengths and widths, given a surface area.
Short Version of Question:
Each of $l$, $w$ and $k$ is a positive integer. Determine all possible values for $l$ and $w$ such that $l \ge w$, and $(k + 1)(l + w - 2k) = 133$.
Long Version of ...
0
votes
0answers
28 views
Convert between View Matrix and Tuple of Camera Position, LookAt Vector, Up-Vector
given a View-Matrix $M$ that can transform world coordinates into camera space, how can I convert between this representation and a more human readable form of Position ($\vec p$), Look-at vector ...
1
vote
0answers
28 views
Vector Tangent to Curve of Intersection
I am having problems solving this.
Find a vector tangent to the curve of intersection of $z = 4x^2 + y^2$ and $z=(27-x^2-y^2)^{1/2}$ at the point $(1,1,5)$.
I'm able to do this kind of thing using ...
0
votes
1answer
20 views
Plotting a function $\phi: C \to R$ in $R^3$ by writing it in terms of $\phi: R \times R \to R$.
I have a complex polynomial $f(z)$ and I would like to plot a 3D graph that takes in $x$ and $y$ (as the real/imaginary parts) and outputs the modulus of the result. How can I write, for example ...
2
votes
0answers
29 views
Big data: 3D clustering with over 40 groups
I am a computational neuroscientist and I struggling over a problem; I have around one hundred 3D matrices (I am working on MATLAB at the moment), each of them is 121x145x121. Any 'cell' stores a ...
2
votes
1answer
71 views
Is this the right equation for this 3D surface?
Is $\frac{\sin \sqrt{x^2+y^2+z^2}}{\sqrt{x^2+y^2+z^2}}$ the right equation for this surface? I am confused what $z$ is doing in there (unless this is an implicit equation). I get something fairly ...
0
votes
1answer
18 views
Commutative applying rotations around three axis
Rotating an object in a 3 dimensional space by euler angles might be intuitive but comes with some problems. First, the order of applied rotations around the different axis matters. Second, there is ...
4
votes
0answers
165 views
How can I solve the Poisson PDE efficiently and fast in cylindrical coordinates?
I am trying to numerically solve the Possion PDE in cylindrical coordinate system.
$$\Delta f = {1 \over \rho} {\partial \over \partial \rho} \left(\rho {\partial f \over \partial \rho} \right) + {1 ...
0
votes
0answers
30 views
How to derive an average Z value among arbitrarily distributed X, Y, Z points
I am triangulating using Delauney algorithm to create a 2D (x, y) flat surface in OpenGL. There are "control points" available, with (x,y,z) values that I need to apply to the triangulated surface to ...
3
votes
1answer
20 views
Finding a point in an ellipsoid
I know the semi-principal axes $(x,y,z)$ of the ellipsoid $E$ (centered at the origin). Given the normalized direction vector $\vec{v}=(a,b,c)$ pointing from the origin to the surface, how can I find ...
0
votes
0answers
145 views
Equation of a 3d cone
Find explicit, implicit and parametric representation of a 3d cone with the following attributes:
Its tip is located at the origin
It opens in the positive direrction of the $Z$ axis
The opening ...
7
votes
0answers
114 views
Visualizing a Calabi Yau
I would like to understand how I can visualize the quintic threefold
$$ z_1^5 + z_2^5 + z_3^5 + z_4^5 +z_5^5 - 5\psi z_1z_2z_3z_4z_5 = 0$$
For a similar problem, Hanson proposes the following:
...
0
votes
0answers
35 views
Collision/intersection of a sphere and triangle.
I have a question from my programming homework, though it would probably be better to as here.
Consider a sphere with radius 3 and center point (1,1,1) colliding with the triangular
face of an ...
1
vote
3answers
196 views
Nullify (zero out, cancel) rotation in an arbitrary axis in a Quaternion
Question:
How do you nullify (zero out) rotation around an arbitrary axis in a Quaternion?
Example:
Let's say you have an object with quaternion orientation $A$.
You also have a rotation quaternion ...
2
votes
2answers
52 views
How to get angle bewteen two vectors in range -1 to 1 without using arc cosine?
Given two normalized vectors in 3d space, how can I get a value from $-1$ to $1$ based on their angle without using arc cosine?
With use of arc cosine, I think this would give me the correct result. ...
3
votes
0answers
54 views
How to solve a distance problem inside of a picture?
sorry for my bad english. I have the following problem:
In the picture you can see 4 different positions. Every position is known to me (longitude, latitude with screen-x and screen-y).
Now i want ...
2
votes
1answer
43 views
Disable one angle of rotation
I'd like to disable one angle of rotation of an object rotating in 3D space. Imagine a camera rotating around and displaying objects as they are in space. I'd like this object to be fixed on the ...
0
votes
0answers
36 views
Proving equivalence intrinsic extrinsic rotations
Rotations can be generated by skew symmetric matrices $[v]^{\times}$ as:
$$
R = e^{\theta[v]^{\times}}
$$
Where $v$ is the normalized axis of rotation and $\theta$ the angle of rotation. Using this ...
1
vote
4answers
45 views
Find the equation of plane containing line described by
Please help me in this really easy task
Find the equation of plane containing line described by
$x+3y-2z=1$, $2x-y+2z=3$, containing point $(1,1,3)$
1
vote
0answers
27 views
Are there 3D tilings of a 3D projective hyperplane or 3-sphere?
I noticed that pentagons tile the projective plane (a spherical dodecahedron). Something they do not do on a flat euclidean plane. Is there analogous 3D tilings (honeycombs) of a 3D projective ...
1
vote
1answer
29 views
What does delta_length mean in this context?
and thanks for looking at this question!
I'm trying to extend a force directed graph layout to not just lay out a graph in 3d (which the following implementation does a fine job of) but to also do so ...
2
votes
1answer
75 views
A controlled trapezoid transformation with perspective projecton
I'm trying to implement a controlled trapezoid transformation in Adobe Flash's ActionScript using the built-in perspective projection facility. To give you an idea of how the effect looks like:
...
2
votes
4answers
78 views
Why can a plane be defined with its normal line?
The title is worded a bit confusingly. I apologize, I just couldn't think of how to phrase it.
Either way, say you have the plane $x+2y-4z=8$
The normal line will have direction $x=1, y=2, z=-4$
So ...
1
vote
1answer
40 views
How to combine bezier curves to a surface?
My aim is to smooth the terrain in a video game. Therefore I contrived an algorithm that makes use of bezier curves of different orders. But this algorithm is defined in a two dimensional space for ...
1
vote
1answer
138 views
About vector form of a line passing through 2 points.
According to my book:
Equation of line passing through 2 points with position vectors $a$ and $b$ is
$$r = a + K(b - a)$$
My question:
If we are given 2 points how do we determine which point is ...
1
vote
1answer
228 views
Moving point along the vector [closed]
I'm making a game. I have came across a problem. I have to move a point along a vector for some distance. Can anyone help me? Any ideas?
2
votes
1answer
78 views
Use pythagoras in a cuboid to find x.
my daughter has a question and I am lost how to solve it.
I have a rectangular box with the following dimensions (see below picture)
Height: $2x-1$
Width: $x+8$
Length: $2x+4$
the line running ...
0
votes
0answers
36 views
isosurface 3d formulas, combining formulas smoothly
I am multiplying together isosurface formulas to make tunnels etc for games, and the intersection of different shapes equals sharp angles that produce mangled triangles and abnormal normals.
it's a ...
0
votes
0answers
95 views
Rotating a system of points to obtain a point in a given place
Given an arbitrary number of points which lie on the surface of a unit sphere, one of which is arbitrarily <0, 0, 1> (which I will call K) in a rotated system ...
3
votes
1answer
104 views
Draw an arc in 3d coordinate system
I have some legacy code which is supposed to draw an arc with constant radius in 3d space however it is drawing the arc in the wrong position. I would like to know and understand the mathematical ...
