Tagged Questions
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 ...
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 ...
-1
votes
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.
3
votes
4answers
145 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
24 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 ...
1
vote
1answer
81 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
27 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 ...
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 ...
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
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 ...
2
votes
1answer
74 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:
...
1
vote
1answer
136 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 ...
0
votes
3answers
71 views
How to calculate triangle-line collision in 3D?
If there is a given triangle (tx1, ty1, tz1), (tx2, ty2, tz2), (tx3, ty3, tz3) and two given point of a line ...
3
votes
3answers
278 views
Tetrahedron problem (proving)
Prove that if $P$ is the intersection of the altitudes of a tetrahedron $ABCD$ and $r$ is the circumradius then $PA^2+PB^2+PC^2+PD^2=4\cdot r^2$.
3
votes
1answer
64 views
Why does aliasing cause loss of a degree of freedom in Euler angles?
I'm reading a book on 3D game math where the author points out that when using Euler angles the same orientation can be reached by doing two different operations; say rotating a cube 90 degrees around ...
1
vote
2answers
113 views
Calculate distance after rotation?
I'll start off by saying that I suck at math.
I'm trying to calculate the distance between a circle and the center of the screen after rotating an image that contains that circle by 45 degrees in 3d,
...
0
votes
1answer
64 views
how to know cylinder volume in pixels?
I have a 3D point cloud representing ad object. I use a 3D cylinder to fit this object in the point cloud, so I check if each point is inside the cylinder and, if it is, then I assign a weight to that ...
0
votes
1answer
94 views
Apply Euler vector to translate vector
This is a problem for 3d graphics programming.
I have an object in 3d space, an airplane, who's position is (x1, y1, z1). The orientation (rotation) specified as a Euler vector in radians, (x2, y2, ...
0
votes
1answer
119 views
How to extend rational parametrization of the circle to three dimensions?
I recently became aware of the rational parametrization of the circle in two dimensions:
$$\left(\frac{1-m^2}{1+m^2}, \frac{2m}{1+m^2}\right)$$
for a unit circle centered on the origin.
I'm ...
1
vote
2answers
254 views
Given a point $(x,y,z)$ and an angle/bearing distance calculate the end point $(x,y,z)$
I'm not very mathematical but I'm working on a 3d program and for this part I simply want to draw a line.
I know the starting vector $(x,y,z)$, the length r of the line and the bearing/angle. I want ...
0
votes
2answers
142 views
3d geometry: triangle 2 points known, find 3rd point
I have a 3d triangle ABC. Lengths AB, BC, and AC are known. Coordinates of points A and B are known. Point C only the y value of the coordinate is known.
I believe there are 2 points that can satisfy ...
2
votes
2answers
111 views
How to calculate the rotation of a vector?
So, let's say I have vector $\vec{ab}$ and vector $\vec{ac}$. How do I calculate the amount of rotation from $b$ to $c$?
Note, this is in a 3D space, of course...
4
votes
3answers
129 views
move a point up and down along a sphere
I have a problem where i have a sphere and 1 point that can be anywhere on that sphere's surface. The Sphere is at the center point (0,0,0).
I now need to get 2 new points, 1 just a little below the ...
0
votes
2answers
347 views
3-D geometry : three vertices of a ||gm ABCD is (3,-1,2), (1,2,-4) & (-1,1,2). Find the coordinate of the fourth vertex.
The question is
Three vertices of a parallelogram ABCD are A(3,-1,2), B(1,2,-4) and C(-1,1,2). Find the coordinate of the fourth vertex.
To get the answer I tried the distance formula, equated ...
2
votes
2answers
167 views
Computing the distance between a point and a line without cross product
Let P be an arbitrary point. Let S be a segment.
Is there any way of computing the shortest distance between P and S without using cross product?
I found a formula that uses cross product. However, ...
1
vote
0answers
70 views
I want to calculate the hypotenuse of a pyramid and need a formula for doing it repetatively
I am a Star Trek geek, and I want to be able to plot courses (distances and direction based on 360x360 plotting) between different stars. I realize that spatial geometry is more difficult than 2D ...
12
votes
1answer
287 views
Floret Tessellation of a Sphere
I'm a programmer looking to create a 3D model of a Floret Tessellation of a sphere, like the one in this picture
Class III 8,11 floret planar net
(source)
If anyone could point me in the right ...
0
votes
0answers
64 views
Determining a point in 3D space
So given a point, a rotation around the y-axis, a rotation around the x-axis, and a distance, how can one calculate the relative point in space? For example, the beginning coordinates are (0,0,0). ...
0
votes
1answer
72 views
How to move a one 3D line from three 3d parallel lines
I have 3 parallel line segments (say AB, CD, and EF are line segments and they are nearly horizontal) lay on 2 slanted planes which have been intersected through the CD. If I projected all the line ...
0
votes
1answer
173 views
3 Dimensional Geometry
Greedy Geoff sawed off a corner of a brick shaped block of Christmas cake, exposing a triangular fresh face of moist rich delicious gateau. He placed the tetrahedral fragment on the table, with its ...
0
votes
1answer
67 views
Calculating a rectangle between 2 points and detecting if a position is within
I'm attempting to basically create a road within a game, and am struggling with how I can detect if my existing geometry is in fact on this road.
Basically I have a list of x,y,z coordinates and if I ...
4
votes
3answers
124 views
How do you detect if a point is in a plane?
Let's say we have 3 points: (-2,7,4), (-4,5,2), (3,8,5) and we want to see if a fourth point, (2,6,3), is in the plane that the previous 3 points made. How would I go about doing this?
0
votes
0answers
42 views
Convert point coordinates
I have to create some transformations for a 3D application but I'm not very good at math.
I have 2 objects in space (let's call them ...
0
votes
1answer
180 views
How to calculate the average direction of 3D elements using normal vectors of their contour surface?
I have a geometry which consists of a number of slender cylindrical elements. Each cylinder is described by a lot of little triangular planes on the surface of the cylinder and I know the normal ...
1
vote
1answer
820 views
Equation for making a circle in 3D space
I have a 3D space with axis $(x, y ,z)$ and I can make a circle in the $xy$-plane.
To make a circle in the xy-plane I currently use spherical coordinates $(r, \theta, \phi)$ where $r = 1$, $\theta = ...
2
votes
2answers
547 views
Point on the left or right side of a plane in 3D space
I have an alpha plane determined by 3 points in space. How can I check if another point in space is on the left side of the plane or on the right side of it?
I need a fast solution for plug-in ...
1
vote
1answer
157 views
How to calculate the direction in which a set of normal vectors (3D) are least oriented?
I have an STL file with thousands of triangular planes with different orientations. What is the best way to calculate the direction in which the normal vectors of the triangles are least aligned?
I ...
0
votes
1answer
37 views
Matrix for transform line into y-axis
I have a line with equation $x_i = a_i t + b_i$, for $i = 1, 2, 3$ (if such way not good i can use any other) with which matrix i can transform this line into $y$-axis? I need to do polenty of ...
1
vote
0answers
69 views
are oblique projections one specific subdivision of trimetric projections?
so i've reaserched a while and come with this broad definitions
a projection is the representation of a 3D object in 2D by the use of "imaginary proyectors"(cameras of some sort).
it has 2 branches, ...
1
vote
3answers
373 views
Decide whether two lines are parallel
I have two lines which I´d like to know whether they are parallel or not in 3D space. Each line is defined using two points $(x_1,y_1,z_1)$,$(x_2,y_2,z_2)$.
Important condition is that there should ...
1
vote
3answers
2k views
How to determine if a 3D triangle given by points is a right triangle?
How do I figure out if a triangle is a right triangle in 3-D space if you are given three points: $P = (3, -2, -3)$, $Q = (7, 0, 1)$, $R = (1, 2, 1)$?
I know that it is an isosceles triangle (two ...
1
vote
2answers
254 views
Distance Formula in Three Dimensions
The distance formula in 3-D space is defined as:
$$|P_1\, P_2| = \sqrt{(x_2- x_1)^2 + (y_2 -y_1)^2 + (z_2- z_1)^2}$$
My question is that if I have 2 points that have negative coordinates, do I have ...
5
votes
3answers
277 views
Rigid-body matching algorithm and clustering algorithm with groups of lines in 3D
I've been struggling with this problem for weeks, and couldn't find an appropriate algorithm to solve it. Could you guys please give me some advices or suggestions in addressing this question. Or if ...
0
votes
1answer
188 views
3D Projection (Perspective). Not what I would expect…
I have some code based on the 3d perspective projection formula I found on wiki.
http://en.wikipedia.org/wiki/3D_projection
It works great... mostly :)
I recently started making the code do z ...
1
vote
2answers
282 views
Polarity of the Surface Normal of a 3D triangle
I have a triangle (defined in 3D space) that has 3 points (p1, p2 and p3).
Is it possible to work out what the polarity of the surface normal would be for the face knowing it lists each point in an ...
0
votes
2answers
151 views
Gram-Schmidt Orthogonalization - does it distort?
I am writing a 3D solar panel positioning programme and have a section of code where I use the Gram-Schmidt Orthogonalization process to go from 3D to 2D for easier calculations.
(For reference, here ...
