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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2answers
40 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: ...
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2answers
40 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
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2answers
100 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 ...
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1answer
59 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 ...
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1answer
18 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 ...
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2answers
31 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 ...
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2answers
36 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 ...
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1answer
116 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 ...
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1answer
74 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 ...
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0answers
47 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 ...
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1answer
43 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 ...
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1answer
37 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 ...
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1answer
35 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 ...
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1answer
38 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, ...
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0answers
15 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 ...
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1answer
68 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 ...
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1answer
44 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 ...
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1answer
55 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) ...
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1answer
148 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 ...
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1answer
80 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 ...
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2answers
56 views

Find the relation between the volumes of a cone and inscribed sphere

I have a question that I've been working upon for a long time but in vain. Can you help me. Determine the relation between the volume of a con circumscribed to a regular tethadron and the volume of a ...
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0answers
34 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 ...
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1answer
101 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 ...
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0answers
62 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 ...
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0answers
83 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. ...
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0answers
35 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 ...
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3answers
47 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 ...
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2answers
128 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 ...
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1answer
30 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 ...
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1answer
20 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 ...
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1answer
369 views

How to find out if four points are on the same plane, only by using distances?

There is a method called Cayley-Menger determinant in order to find if 3 points are collinear, 4 points are coplanar etc. provided that all the pairwise distances are given. However, in 2-D, there is ...
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0answers
133 views

Find the linear (vertical) acceleration using a three axis accelerometer.

I genuinely apologise for what may be a poorly worded question. I'm extremely tired but have a ridiculous huge and important project due in on Monday for my degree. Thank you in advance for any help ...
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0answers
26 views

What is the offset curve of a 2D slice of the 3D offset of a twisted swept figure

I have a simple 2D shape as below helically swept. I then do an offset in 3D from the surface. to get if I take a 2D cross section I then get As you can see the offset curve of the 2D ...
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0answers
37 views

How to define a binormal equation using 3D coordinates, with given sine wave function?

I am attempting to implement in code the math and functions found here: http://http.developer.nvidia.com/GPUGems/gpugems_ch01.html So this question is contextual to that article, I'm sorry for that, ...
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2answers
37 views

Scale a Point onto Plane

I'm trying to find the scale factor that scale a point onto plane in 3D Space. I have the following information: Point on a plane: $a = (x_1,y_1,z_1)$ Plane equation: $P\colon Ax + By + Cz +D =0$; ...
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1answer
39 views

How to Create a Plane Inside A Cube

I have a $e \times e \times e$ cube and I want to create random planes with equation $ax + by + cz + d = 0$ inside this cube. I will put random points on those randomly created planes as well. Here ...
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1answer
50 views

Equation of a plane through intersection of two and parallel to other

I have got two planes $$x+y+z=1$$ and $$2x+3y-z+4=0$$ . I am required to find a plane by intersection of two and parallel to $x$ axis . I think the plane parallel to $x$ axis so Simply $P1+kP2=0$ ...
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3answers
66 views

3D triangle computer graphics

We are given a 3D triangle with vertices $(0,0,0), (5,0,10), (0,20,0)$. What is the $z$ value of the point in the triangle with $x=3, y=1$? How do we find the $z$ value?
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1answer
221 views

Best way to plot a 4 dimensional meshgrid

I have $4$ variables $X$, $Y$, $Z$ and $C$, and I want to plot these on a graph. Usually I would just plot the surface $X$, $Y$, $Z$ and then use color to represent the $4$th dimension, as shown ...
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1answer
69 views

3D Graphing--finding an equation given a graph

I'm having trouble finding a reasonable equation for this graph: http://i58.tinypic.com/15gtrn7.png The x axis is the horizontal, y-axis is the axis coming out of the screen, the z-axis is vertical. ...
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0answers
103 views

Best closed convex surface fitting N points in 3D

First. It's easier to understand the problem by describing the application where it arises from. We have a convex body $B$ in $\mathbb{R}^{3}$ and measure points on its surface. The measurements are ...
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0answers
57 views

Solve equation for best fit plane

It was posted by joriki that "Subtract out the centroid, form a 3×N matrix X out of the resulting coordinates and calculate its singular value decomposition. The normal vector of the best-fitting ...
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1answer
47 views

Classifying point stabilizers for the groups associated with 3D model geometries.

For those who have the book, this question is regarding p181 in Thurston's "Three Dimensional Geometry and Topology" (although I will do my best to summarize it). Basically, there's an entire ...
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1answer
42 views

Find $z$ of a point in a plane in 3D space

Say for example, I have 4 points which I know the coordinates to, how can I find a fifth point that lies somewhere within them? E.g, if $A(0,0,a)$, $B(1,0,b)$, $C(1,1,c)$ and $D(0,1,d)$ lie in a ...
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2answers
84 views

How to Represent a 3D Line under Polar Coordinates

In one of my applications, I need to represent a line under 3D polar coordinates system. In 2D, we can define a line by a distance to the origin and then a angle indicating the direction of the line ...
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1answer
94 views

Big axis of an ellipse

I drew a circle in this square and I transformed them (view in 3d). How to find the angle between the big axis and $y$ or $x$ axis? Blue plane rotated by 36° around $y$ axis; azimut is 30° and ...
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2answers
178 views

Find tangent vector to surface given a point on the surface and its normal vector (for a sphere)

I need to know how to find a tangent vector to a point on the surface of a sphere if I am given the point P and the normal vector at that point N. I know that there are many possible tangent vectors ...
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2answers
42 views

Problem with vector multiplication

I have this plane problem and the answers are released for it. I don't understand this specific part: Why does : (i + 4k) x (3j - k) = -12i + j + 3k. I tried using the cross product method, however, ...
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2answers
85 views

solving 3-d coordinates from x, y and z distance

I working with WiFi positioning and i want to know the exact coordinate where I am. Here is the problem..
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2answers
131 views

What is (fundamentally) a coordinate system ?

Consider the following construction of vectors and points. Let's start with a vector space, or more specifically a coordinate space $F^N$ over a field $F$ and of $N$ dimensions. The elements of this ...