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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1
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1answer
198 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
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1answer
45 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
93 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
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2answers
154 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
238 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
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1answer
57 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
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3answers
86 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 $R$, ...
-1
votes
2answers
85 views

Is it possible to find the coordinates of a point in 3D space, given its distance from a known point?

Is it possible to find the coordinates $(x,y,z)$ of a point in $3d$ space when given: A) the unknown point is $(x,y,z)$. B) the known point is $(a,b,c)$. C) the distance between the two points is ...
1
vote
1answer
98 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
89 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
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1answer
376 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, ...
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2answers
3k views

How to prove that two lines in 3D are not parallel and do not intersect; also, how to find the distance between them?

Problem Given two lines: $$(l_1)=(x,y,z)=(3,-1,2)+t(1,1,0)$$ $$(l_2)=(x,y,z)=(0,5,2)+t(1,-2,1)$$ Explain why these two lines are not parallel and why they do not intersect each other. Also, find the ...
1
vote
1answer
2k 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
40 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
208 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, ...
6
votes
3answers
2k 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
211 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
51 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 ...
1
vote
2answers
82 views

How to find angle of plane $7x+13y+4z = 9$ with $xy$ coordinate plane?

How can I calculate inclination of $7x+13y+4z = 9$ with $X-Y$ plane As for as I understand from question is that the angle of plane $7x+13y+4z=9$ with $ax+by+0z=d$ for $(XY)$ plane.
1
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1answer
235 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
270 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.
1
vote
1answer
48 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 ...
2
votes
0answers
74 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
489 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
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2answers
808 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
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0answers
491 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
492 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
149 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
273 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
401 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
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1answer
138 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
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2answers
241 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
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2answers
3k 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
508 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, ...
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0answers
206 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 ...
1
vote
1answer
259 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 ...
1
vote
2answers
331 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
218 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
622 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
134 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
114 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
387 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 ...
3
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0answers
137 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 ...
0
votes
1answer
215 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 ...
1
vote
1answer
580 views

Finding a 3D transformation matrix based on the 2D coordinates

I have a square with the length of the sides being 1. This square is transformed by an unknown transformation matrix in the 3D space and then projected back to the plane (the projection is known). I ...
3
votes
0answers
266 views

Convolution theorem in 3D

Suppose to have a 3-dimensional discrete grid. I would like to convolve it with a 3-dimensional tensor (a 3x3x3 "cube"), applying the convolution theorem. Hence, I should apply a Fourier transform to ...
0
votes
0answers
268 views

Distance between two objects in a picture

lets say I have a photo that has a picture on a wall and a book upright on the desk. now i know the size of both of these objects. I want to find the distance between two of them on the photo, I was ...
0
votes
1answer
148 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 ...
2
votes
3answers
329 views

3D graphic in vector format

Please recommend a program that can build a graphic of a 3d function and save it to some vector file format (SVG, EPS/PostScript, WMF etc.) I found only Madagascar software, it is free, but it was ...
1
vote
2answers
262 views

Equation of a line on a plane…

Hi this question belongs to camera projections but i cannot understand the mathematics... i am not getting how the cross product of two vectors (underlined in red) gives the equation of a ...