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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1answer
20 views

How to rotate a line in 3d space? [on hold]

I am trying to figure out direction vectors of the arrowheads of an arrow. Basically I'm given a normalized direction vector ...
0
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0answers
35 views

Quarternions from MPU and circumference of circles

First I should mention that my math skills are super basic. I do not understand formulas but I do understand pseudo code, C, C++, and other programming languages. I've been working on a electronics ...
0
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1answer
40 views

How do I multiple these matrices together?

As a personal brain exercise, I've recently been trying to work out the math involved with rotating vertices around an arbitrary axis in 3D space. To do so, I've been relying very heavily on the ...
0
votes
2answers
242 views

Angle between planes

If the angle between two planes is $\alpha$ , why is the angle between normal of the two planes is $\pi - \alpha$ ? Also Why angle between a line and normal to a plane is $\pi/2 -\alpha$ if angle ...
0
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0answers
16 views

Find the normal of a polygon with vertices that are not linearly independent in 3d

For example, take the vectors: $(1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15)$ What would the normal to the polygon be? I'm guessing it would be $(0,0,0)$? For vertices that are linearly ...
1
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0answers
27 views

Counting the number of cubes in an isometric view

I had seen questions in a sample aptitude test, where an isometric view of an object made up of cubes was given, with some of the cubes removed. We were supposed to count the number of cubes present ...
1
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1answer
16 views

equation of a plane through 2 points and parallel to a line

what is the equation of a plane passing through 2 given points (p 1) and (p 2) and parallel to a given line L 1? i know how to find the equation of a plane passing through a point with position ...
0
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1answer
30 views

Determine if a point is within two planes [closed]

I have a point P and two planes defined by three vertex each. How can I determine if P is between the two planes?
0
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1answer
13 views

Finding the coordinates of a point on a line that produces the shortest distance to another point in 3 dimensions.

I have a question with two parts and it looks like the following: a) Determine the distance from point $A(-2, 1, 1)$ to the line with the equation $\vec{r} = (3, 0, -1) + t(1, 1, 2)$, $t\in \Bbb R$ ...
2
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2answers
34 views

Finding an equation of a plane a certain distance from a given plane

I just wanted to know the methodology of how to solve for the equation of a plane that is some distance from some given plane. Thanks. Any help is appreciated
0
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2answers
33 views

How do I calculate the inverse of these matrices?

In learning how to rotate vertices about an arbitrary axis in 3D space, I came across the following matrices, which I need to calculate the inverse of to properly "undo" any rotation caused by them: ...
1
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2answers
31 views

Is the rhombic dodecahedron the only isohedral polyhedron that tiles 3-space (other than the cube)?

Is the rhombic dodecahedron the only face-transitive (or isohedral, i.e. all faces are the same) polyhedron that seamlessly tiles 3-dimensional Euclidean space (other than the cube)? I'm looking ...
0
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1answer
22 views

rotation matrix to axis angle

from wikipedia the above rotation matrix has a rotation of -74 degrees. What does it mean "around the axis (−1⁄3,2⁄3,2⁄3)"? How can I determine how many degrees is rotated on X axis, Y axis and Z ...
1
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1answer
15 views

Make a point orbit another point, given time and a normal.

I am working in 3D space. I am trying to make a solar system model. known variables: center of orbit, C (x,y,z) normal, perpendicular to the orbit, N (x,y,z) radius of orbit, R time, position ...
1
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2answers
21 views

Local max/min points, partial derivatives

I'm having a lot of problems with figuring out how to properly do max/min with partial derivatives. To my knowledge, we have: $$D(x, y) = f_{xx}(x, y)f_{yy}(x, y) - (f_{xy}(x, y))^{2}$$ With the ...
0
votes
2answers
20 views

How to find a normal vector from an equation in the form f(x,y)?

If I have an equation $f(x,y)$ which given the $x$ and $y$ coordinate, it gives you the $z$ coordinate. How can I find the normal (directional) vector of the the point $(x,y,f(x,y))$? This would be ...
0
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2answers
1k views

Calculate distance, knowing actual and perceived size

What's equation would I use to calculate distance to an object, if I know it's actual and perceived size? Say there is a line, and I know it's actual length is 65 (units), I perceive it as 62 ...
0
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0answers
9 views

Creating a Cube-based 3-Dimensional Game [migrated]

I am trying to create a 3-dimensional game that is based entirely off of cubes of the exact same size. I wanted to learn how to make my own 3-dimensional game using only 2-dimensional game libraries. ...
2
votes
1answer
200 views

How to recover three successive rotations of a vector

I have a vector, which I rotated with respect to $x$, $y$ and $z$ axes, respectively. Now I want to recover this operation, that means I want to bring it to the previous position by rotating it with ...
1
vote
1answer
31 views

Incenter of Triangle in 3D

I'm trying to figure out how to find the incenter of a triangle with (x, y, z) coordinates for the verteces. I can find the lengths of the sides and the radius of the incircle from that, so I've ...
0
votes
1answer
25 views

Finding the counter-clockwise direction of points in 3d

I have a set of 5 points of a polygon in 3d. I want to order these points in a counter-clockwise direction. How do I do this? In 2d, to check if two points are ordered counter-clockwise or ...
1
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1answer
21 views

texture mapping from a camera image to a 3D surface acquired by a kinect

I have the following problem: A kinect camera capture a 3D surface and save it as a .obj files containing all the positions of the vertices (in the kinect coordinate system). If I take a picture ...
1
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1answer
33 views

Volume of the Region bounded by $y = 2x^2 +2z^2$ and the plane $y=8$

I have the find the volume of the region bounded by the paraboloid $y = 2x^2 +2z^2$ and the plane $y=8$. Is the volume (using triple integrals) just ...
1
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0answers
14 views

Find the volume between a hyperboloid and a cylinder

I'm trying to find the volume bounded by the graphs of $z = 0$ and $z = h$, outside of the cylinder $x^2 + y^2 = 1$, and inside the hyperboloid $x^2+y^2-z^2 = 1.$ I have tried to use cylindrical ...
1
vote
1answer
30 views

Centre of the sphere

A variable plane passes through a fixed point $(a,b,c)$ and cuts the coordinate axes at $P,Q,R$. Then the coordinates $(x,y,z)$ of the centre of the sphere passing through $P,Q,R$ and the origin ...
8
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6answers
17k views

Recommended (free) software to plot points in 3d

I am looking for (preferably free) software to: 1) plot 3d points read from a file. A scatter plot would be fine. 2) Optionally color the points by a property - also read from the file It would be ...
0
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1answer
33 views

How to solve this integral in 3D?

I am willing to compute the Fourier transformation of the following function: $$ \Phi(r) = (I\Delta - \nabla \nabla )[r\operatorname{erf}(\xi r)] $$ Where, $r = X-X_0$, $\xi$ is a positive constant, ...
0
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1answer
20 views

How to rotate a 3d vector to be parallel to another 3d vector using quaternions?

I have a vector (a,b,c) and another vector (d,e,f). I'm trying to rotate (a,b,c) so its parallel to (d,e,f) using quaternions. I need help understanding how I would do this. I have so far that a ...
1
vote
0answers
8 views

Why is tree traversal the fastest ray-box method?

I'm learning ray tracing (the problem of intersecting a ray, aka a vector, against a 3D box defined by a max and a min point) and I'm wondering: why is a tree traversal (e.g. bounding volume ...
0
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1answer
24 views

Find vector rotated on 3D plane

I don't have access to a computer so I can't give pictures but I will try to make this easy to visualize. Suppose I have a vector $n$. I will now draw a plane normal to this vector that and have that ...
2
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2answers
1k views

How to calculate volume of 3d convex hull?

Convex hull is defined by a set of planes (point on plane, plane normal). I also know the plane intersections points which form polygons on each face. How to calculate volume of convex hull?
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2answers
86 views

Finding the missing vertex $(x,y,z)$ of a rectangle whose other vertices are defined.

How do I find the missing fourth vertex $D$ of a rectangle, which has three vertices defined? The Equation of the plane being $ax+by+cz+d=0$ Where, $a = (By-Ay)(Cz-Az)-(Cy-Ay)(Bz-Az)$ $b = ...
0
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1answer
26 views

clockwise or counter clockwise in 3D

I have two different situation that I need to make distinction between them (shown in the picture). In other words, in (A) points 3 and 4 are in right and left side of line 1-2. However, in case (B) ...
1
vote
1answer
589 views

Calculating an average plane from a series of points using Numpy [closed]

Given N, 3D position vectors, I want to find the best-fit plane of those vectors. I found a suggested answer here that said: Calculate the average of the points (easy) Calculate the Covariance ...
0
votes
1answer
20 views

Find a 3D vector given the angles of the axes and a magnitude

I would like to know how one would find a point from the angles of three axes and a magnitude. I know how to do this in 2D: $(\cosΘ * m, \sin(Θ) * m)$. However, I would like to know how this would be ...
1
vote
1answer
225 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
0answers
23 views

Shooting a grenade - angle throwing

In my 3D simulation/game I need to shoot a grenade from a grenade launcher. The movement of the grenade is already setup by someone else. all I need is to give him the pitch angle of the grenade ...
0
votes
1answer
188 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, ...
1
vote
1answer
27 views

Area of circle formed when sphere is sliced by a plane

First off, when a sphere is cut by a plane, is a circle always formed or does a ellipse get formed in some cases? If a circle is always formed, how do you prove it? Next, how would you find the area ...
0
votes
1answer
302 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 ...
2
votes
1answer
280 views

points of intersection on a randomly situated plane and ellipsoid (spherical) in 3d space

if i have an ellipsoid and a plane oriented in any way in a 3 dimensional coordinate system, and they intersect; is there a way to find an equation that describes (or at least approximates) all points ...
4
votes
3answers
13k views

how to calculate area of 3D triangle?

I have coordinates of 3d triangle and I need to calculate its area. I know how to do it in 2D, but don't know how to calculate area in 3d. I have developed data as follows. ...
0
votes
0answers
27 views

Distance from a point to the walls of a cube in 3D

I have defined six different planes that constitute a cube($6$ plane equations). I place an object within the cube at a point $P_1 \equiv (X_c,Y_c,Z_c)$. There are $6$ cameras on the object pointing ...
0
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3answers
41 views

Determining if a point is inside two planes

I have two planes(Plane 1 and Plane 2) the normals ($n_1$ and $n_2$) of which are known to me. How do I determine if a point is inside the two planes? By inside I mean the 3d space between Planes 1 ...
0
votes
0answers
26 views

Converting Euler Angle z-y'-x'' sequence to heading

I'm trying to convert a set of Euler Angles to a heading $(0-360)$ degrees. The Euler Angles use the $\ x-y'-x''$ sequence headings, using $\ \psi, \theta, \phi$ as the rotation angles, respectively. ...
0
votes
0answers
20 views

Partition of the 3d space with circles?

Does it exist a partition of the 3d space with circles of positive radium? I know the answer is no for a plane, but I can not transpose my demonstration to the space and I have no clue on how to do ...
-1
votes
0answers
29 views

Show that if a, b, c are three dimensional vectors, then…

Show that if $a, b, c$ are three dimensional vectors, then $$(a \times b)\cdot[(b \times c) \times (c \times a)] = [a \cdot (b \times c)]^2$$ Hint: Use identities.
0
votes
2answers
59 views

Finding distance between lines in 3D

Find the distance between the lines $L1$ and $L2$ where $$L1: \frac{x-1}{2}=\frac{y-2}{-3}=\frac{z-3}{4}$$ and $$L2: \frac{x+1}{3}=3-y=\frac{z+5}{5}$$ I need to first show that the lines are skew and ...
0
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1answer
21 views

Linear Algebra: finding specific linear combinations which meet the criteria

Consider any three vectors u,v,w in 3-dimensional space s.t joining the three vectors by straight lines forms a triangle. Under what condition on c,d,e will the combination cu + dv + ew fill the ...
0
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1answer
17 views

This is regarding 3d parametarization and vectors.

Generally, I have a hard time conceptualizing how to sketch a vector that looks like $(\cos t, \sin t, t)$. How do I approach this? Usually, in an examination, there are really small bounds given so ...