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
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 $PA^2+PB^2+PC^2+PD^2=4\cdot r^2$.
0
votes
0answers
35 views
Turn any shape to circle
I'm looking at trying to calculate and re position 3d vectors to align in a new position to form a circle.
I've achieved this already however only when all points are evenly distributed in the same ...
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
68 views
Calculating new vector positions
I'm using the following formula to calculate the new vector positions for each point selected, I loop through each point selected and get the $(X_i,Y_i,Z_i)$ values, I also get the center values of ...
0
votes
0answers
38 views
Determine equation for 3D surface defined by 4 2D curves at retangular bounds
Could somebody please help me determine the equation for a 3D surface defined
by the following curves?
y = 0
$$
z = -(A/100)x^1 + A
$$
y = 100
$$
z = (Cx)^{log(100C,(100-B))} + B
$$
x = 0
$$
z = ...
1
vote
1answer
64 views
Calculate vector position
I'm trying to calculate & move vertices to their average "radius" and form a circle from these new positions.
Example: I have 8 vertices selected, I have a little script in Maya that will iterate ...
0
votes
1answer
37 views
New vector position
How can I calculate the new position of a 'point', with just a distance value coming from the center of the selection.
Example: I have 8 vertices selected, I have a little script in Maya that will ...
0
votes
1answer
63 views
How to get Euler angles where an initial value of Euler angle is set as baseline
I have a sensor which gives me Euler angles (roll,pitch,yaw). There is a baseline value of Euler angle (assume it is 5,10,15) at the beginning.I want to calibrate this baseline values from all ...
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,
...
4
votes
5answers
109 views
Moving on the surface of a cube
A $3 \times 3$ cube is composed of $27$, $1 \times 1$ cubes. Moving along the surface of the larger cube, how many ways are there to get from the closer top-left vertex, to the further bottom-right ...
3
votes
1answer
46 views
Books for mathematics used in computer games.
I'm looking for a good book (idiot proof) for learning all the magic behind computing matrices, quaternions, euler angles, orientation in 3d space and more...
Book needs to have examples and ...
0
votes
3answers
48 views
are 12 different rotation matrix the same?
If I want to rotate a vector $V$ from coordinate system $A$ to $B$, I could use the rotation matrix by $V_B=R\cdot V_A$, where $R$ is the rotation matrix. There are many rotation sequences for $R$, ...
0
votes
2answers
36 views
Points of coordinate in a $3$-d space
How can I find the coordinates $(x,y,z)$ in a $3d$ space when,
A) the unknown point is $(x,y,z)$.
B) the known point is $(a,b,c)$.
C) the distance between the two points is $D$.
1
vote
1answer
67 views
How can I find the position vector?
There are two planes intersecting at a line.
Plane 1: $x - 2y + z - 9 = 0 $
Plane 2: $x + y - z + 2 = 0$
There is a point $A = (p, q, 1)$ on the line of intersection.
How can I find $p ...
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 ...
1
vote
1answer
80 views
How to generate an ordered list of vertices of a cube from a face and a normal vector
Consider a cube with faces we'll call "left", "right", "front", "back", "top" and "bottom".
The cube can be described by $0 \le x,y,z \le 1$.
To name the faces, we'll say $x$ extends to the right, ...
1
vote
1answer
486 views
How to find perpendicular distance from point to plane in 3D
The line $L_1$ passes through point $A$ whose position vector is $3i - 5j + 4k$, and is parallel to the vector $3i + 4j + 2k$. The line $L_2$ passes through the point $B$ whose position vector is $2i ...
2
votes
1answer
38 views
least number of planes intersecting a finite number of points in space, but not intersecting origin.
Let
$$\mathbb{R}^*=\mathbb{R}-\{0\}$$
and
$$N=\{0,...,n\}$$
and
$$\mathcal{M}=\{ A\subseteq \mathbb{R}^3\times\mathbb{R}^* \mid (\forall\mathbb{x}\in N^3:\mathbb{x}\ne 0)(\exists(\mathbb{a},d)\in ...
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
0answers
25 views
Phong Reflection Model Parameters
Question:
Can anyone refer me the Phong reflection model parameters for a face image taken for web-cam?
Details:
I am doing 3D reconstruction of 2D images using 3D Morphable Model as in this ...
2
votes
2answers
134 views
Rotating one 3-vector to another
I have written an algorithm for solving the following problem: Given two 3-vectors, say: $a,b$, find rotation of $a$ so that its orientation matches $b$.
However, I am not sure if the following ...
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 ...
2
votes
1answer
48 views
shortest distance b/w 2 lines
I have 2 Question on $3-D$ Geometry
(1) The point on the Line $\displaystyle \frac{x-3}{1}=\frac{y-5}{-2}=\frac{z-7}{1}$ which is Nearest to the Line
$\displaystyle ...
0
votes
0answers
40 views
scaling items to match field of view (FOV)
I am overlaying some clickable hotspots on top of a proprietary panorama viewer application, and I need to make sure that the hotspots scale according to the changing field of view as the user zooms ...
1
vote
1answer
83 views
Determining camera orientation (possibly using calibration images).
I need to generate a camera calibration pattern. Cameras are expected to be placed at an average height of 15 to 30 feet above ground pointing downwards at roughly 30 degrees. These cameras are ...
0
votes
2answers
75 views
Reflecting a point by a line in $\mathbb R^3$
I would like to know if it's possible, given the vector equation of a line and the coordinates of a point, whether it's possible to reflect the point by the line.
0
votes
1answer
23 views
How many faces can have at most the intersection of two rectangular frustums?
In a 3D context, I want to evaluate the intersection of two rectangular frustums.
The intersection of those two frustums will be a convex polytope, I think.
What will be the maximum number of faces ...
1
vote
0answers
38 views
How do you call a 3d convex shape made of 8 arbitrary points?
Is there a name for a 3d convex shape made of 8 arbitrary points ?
That would be like a cube or a box, except that the distances would not necessarily be equals, neither the angles necessarily be ...
0
votes
1answer
173 views
Solving vector equations with dot products
I'm working on a triangle-triangle intersection algorithm using this article ("The Line Intersection of Two Planes" part). The problem is that I don't know how to solve vector equations with dot ...
1
vote
2answers
255 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 ...
1
vote
0answers
179 views
Rotating co-ordinates in 3D
Suppose I have 3 axes, $x$, $y$, and $z$ such that $x$ is horizontal, $y$ is vertical, and $z$ goes in/out of the computer screen where $+$ve values stick out and $-$ve values are sunken in.
Suppose ...
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
1answer
251 views
Expression of the Equations of 3D Egg Shape in terms of degrees
I'd basically like to have 3D version of this article section or this section. So for my case, there are two angles for latitude and longitude to construct 3D egg. Any hint to extend the formula to 3D ...
0
votes
1answer
86 views
Is there a formula to know the angle of an object, on a Cartesian plane, when it is rotated by arbitrary x, y, z degrees?
Example: If I have a line rotated (at its center) by -45 degress on the x, y, and z axis what formula would I used to determine what angle that object is at if you put it back on a cartesian plane?
...
0
votes
2answers
108 views
What does negative sine mean in this diagram?
I thought cos was x and sin was y. In quadrant two, cos is negative and sin is positive. Why does this diagram have a negative sign as the x-coord and cos as the y coordinate for q prime's vector?
...
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 ...
0
votes
0answers
37 views
Find point in $3D$ space only using $3$ rotation inputs and distance
I'm hoping somebody can shed some light on a problem I am trying to solve. As its been a few years out of school my mathematic skills aren't as sharp as they used to be.
My problem...
In $3D$ space, ...
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 ...
0
votes
1answer
73 views
Intersection of a line segment and a paraboloid in 3D
Suppose I have a line segment $L$ in 3D:
$$x=a_1(1-t)+b_1t$$
$$y=a_2(1-t)+b_2t$$
$$z=(a_1^2+a_2^2-k_1^2)(1-t)+(b_1^2+b_2^2-k_2^2)t$$
Because $L$ is line segment then $0\leq t\leq 1$.
And defining ...
0
votes
1answer
67 views
Identify and sketch the quadric surface?
I'm stuck trying to figure out which type of quadric surface this equation is:
$$\dfrac{x^2}{16} - \dfrac{y^2}{9} - \dfrac{z^2}{1} = 1$$
I have narrowed it down to a hyperboloid, but cannot ...
1
vote
2answers
76 views
3D objects in 2D drawing: How to get the size of a box relative to a known plane?
Sorry if this is a really badly worded question. Say you have a box of unknown size, and a planar object of a known size (say, a credit card).
You arrange these object somehow (probably with the card ...
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
208 views
Ray Plane Intersection Calculation
I am currently having issues with calculating plane intersection of a ray.
I start with the following equation
$P = P_0 +tR_t$
$R_t$ is the Unit Vector of the Trajectory.
Now we have a plane ...
2
votes
0answers
60 views
Visualizing and manipulating 4-dimensional data with 3D technology
It is possible to visualize 3 dimensional data (like a scatter plot) by projecting it on a 2 dimensional screen in a way that allows to interact with it in an intuitive way.
Is it possible to ...
