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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3
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2answers
20 views

What formula will tell if three vertices in 3d space are ordered clockwise or counter-clockwise from the point of view of a camera?

Assuming 3 ordered vertices in 3d space and a camera looking toward those points. What formula will tell me if they are seen clockwise or counter-clockwise in relation to their order?
0
votes
1answer
33 views

Implicit 3d plot with depending bounds

I would like to plot this plane ($k1,k2,k3$ are constants): $x-k1=0$ such as $x=k1..n$ ; $y=(z-k3+k2)..n $; $z=k3..n$ The difficulty is that second variable y depend on z. I was trying to use Maple ...
2
votes
1answer
18 views

What is the spherical parametrization of an ellipsoid NOT centered in the origin?

I would like to know how to parametrize an ellipsoid not centered in the origin, but with its axes parallel to the main axes of the reference system. The result I am looking for would be an ...
0
votes
0answers
19 views

Volume of a tetrahedron given length of edges.

I found this method to find the volume of a tetrahedron given the length of edges on Wikipedia I found this Interesting, and was looking for a formal proof, but didn't find it anywhere. Could ...
0
votes
1answer
27 views

Test if a point is inside a 3D cuboid

I have a cuboid in 3D space, it is not regular at all. I do have the coordinates of its 8 vertices and my problem is how to determine a given point coordinate is inside or outside this cuboid. I ...
0
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0answers
22 views

Isometries of S^3 and some Lie algebras

By considering $S^3$ as the group of unit quaternions, and letting it act on itself from both the left and right, one can get an isomorphism $SO(4)\cong (S^3\times S^3)/C_2$, where the $C_2$ subgroup ...
-1
votes
1answer
16 views

Get unit vector from point in direction of angle in 3d [closed]

given a Point $P(x,y,z)$ and an angle $\phi(\alpha,\beta,\gamma)$, how to I get a unit vector from $P$ going in the direction of $\phi$? Thank you for any help!
0
votes
1answer
18 views

When are two 3D Lines parallel in Plücker matrix form?

When are two lines in 3 dimensional space parallel, when the lines are both represented by Plücker matrices $L$ and $L'$. I'm trying to prove the solution to this question: ...
0
votes
1answer
25 views

Torus helix radius change equation

If we draw a closed helix trajectory on the surface of a torus (with helix center axis corresponding to that of torus), the radius will cyclically change between inner and outer radius (r and R). Can ...
0
votes
0answers
19 views

Signed angle bewtween two normals

I have two abitrary planes in 3D space which share two vertices. Each plane has a unit normal and boh planes follow the same 'handedness' which describes the 'up' side of the plane. The line between ...
0
votes
1answer
16 views

Number of variables and dimension of a function

Why is a function $f(x)$ called a single-variable function if it has coordinates represented by $x$ and $y$? Can it be called a 1D function if its plot is 2D? Subsequently, can two-variable functions ...
0
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0answers
13 views

Intersection of a Plane with the Riemann Sphere

While reading Fundamentals of Complex Analysis by Saff and Snider, I came across an example (see page 47, edition 3) where it is shown that "all lines and circles in the $z$-plane correspond under ...
1
vote
1answer
21 views

Why 2 equations of the form F(x,y,z) = 0 for one 3D curve

It says in my analysis 2 book that a curve is given by $F_1(x,y,z) = 0$ and $F_2(x,y,z) = 0$. Why do we need two equations of $x,y,z$ To define a curve in 3D, shouldn't one be enough?
0
votes
2answers
47 views

The easiest way to find distance between point and a line defined by two points in 3D

Let's assume I have two points with coordinates $(x,y,z)$ and $(x_1,y_1,z_1)$ and there is line between them. I am given a point with coordinates $(x_2,y_2,z_2)$. What's the easiest way to calculate ...
0
votes
1answer
22 views

Rotating a plane defined by a normal and a distance from the origin around an arbitrary point in 3D space

I have a plane defined by its normal and its distance from the origin. I have a rotation matrix and a point in 3D space around which to do the rotation. What formula will allow me to do the rotation? ...
0
votes
2answers
24 views

Considering a convex polygon lying on a plane in 3D space, how can I know if a point on that plane lies inside or outside that polygon?

I have a plane in space and a polygon in it. I know the position of each vertices making the polygon. I also know the position of the point on the plane. How can I know whether the point is inside or ...
1
vote
3answers
258 views

Center of Mass in 3D object?

How would I find the center of mass in a 3D object (a "spinning top" or "dreidel") that consists of a cylinder welded on top of a box welded on top of an upside down cone? Assume building material is ...
1
vote
2answers
15 views

Make a multivariable function continuous

What can we do with this function, so the function will be continuous in $(0,0)$? $f:\mathbb{R}^2\rightarrow\mathbb{R}:(x,y) \mapsto \frac{x^2+y^2-x^3y^3}{x^2+y^2}$ What I think we should do, is: ...
1
vote
3answers
62 views

Showing that a Unit Speed Curve is a Circle.

In my recent differential geometry tutorial, we were given the question: Given the unit speed curve, $$\boldsymbol{r}(s)=\left(\frac{4}{5}\cos(s),1-\sin(s),-\frac{3}{5}\cos(s)\right)$$ show that ...
1
vote
0answers
22 views

Equation for Circle in 3D Space Given Center, Radius, and Point

I'm looking for how to derive the equation of a circle, in 3D space, given the following information: The Center Point The Radius One point on the circle I understand that this is functionally the ...
-1
votes
2answers
89 views

3D Geometry Problem

If we have 4 equal sized spheres with radius $R$ arranged surrounding another smaller sphere such as to make a triangular pyramid from the centers of the $4$ spheres with radius $R$. The radius of ...
1
vote
1answer
24 views

Algorithm for solving line line intersection in 3d

I am trying to find an algorithm that a computer can execute that finds the intersection point between two lines each defined by a point on the line and a direction vector. Does anyone know of one? It ...
0
votes
0answers
13 views

For an app teaching about polyhedra, what are some core characteristics to include?

For fun: I'm building a 3d app that teaches about polyhedra. What should I include? The obvious didactic elements for each polyhedron would be: Fundamental polygon's Vertices 
Edges
 Faces
 (and ...
0
votes
1answer
47 views

Drawing 3D stomach structure in Matlab [closed]

I would like to plot a 3D structure representing the stomach in Matlab. A sketch of what it should look like is here: http://thoracicsurgery.stanford.edu/patient_care/images/normal-stomach.jpg Still, ...
2
votes
1answer
56 views

Is it possible to accurately calculate an irregularly shaped frustum's volume?

I have the following water basin Now imagine this basin is filled with water to the top, is there anyway to accurately calculate the volume of water stored in it using only top and bottom areas A1 ...
0
votes
1answer
35 views

Counting points in/on cuboid

Given a cuboid that extend in x,y,z axis such that |x|≤N, |y|≤N, |z|≤N where N is given and can have value up to 10^9.Now a shooter is standing at origin (0,0,0).He need to shoot on any of the ...
0
votes
2answers
23 views

Rotate and translate a line so that it passes through two given points

I have 2 point and a line segment in 2d space. The line only rotates and translates using its mid point. How do I calculate the translation and rotation required for the line to be touching the 2 ...
2
votes
1answer
27 views

Surface of 3D Triangle

The coordinates $A(-1,0,2), B(2,-1,3)$ and $C(4,0,1)$ are the corners in the triangle $ABC$. a) Find the length of the sides in the triangle. b) Find the area of the triangle. Now I'm able to ...
3
votes
0answers
31 views

Is it possible to create a volumetric object which has a circle, a square and an equilateral triangle as orthogonal profiles?

This question was posed to me by a friend (formulated as creating a peg to fit perfectly into holes of these shapes), and after an experiment in OpenSCAD it seems it is not possible - either one ...
0
votes
0answers
24 views

Get Vector From Angle In $3D$ Space

I have a camera angle in $x,y,z$ with values between $0$ and $360$, I'm trying to compute this into an 'aim vector' which would have values between $0,0,0$ and $1,1,1$ depending on what the angles ...
2
votes
1answer
18 views

Dot product of any point on plane and its normal

I was trying to find the distance between a point and a 3D line with parametric equations. On the web, I found a video detailling the steps. https://www.youtube.com/watch?v=9wznbg_aKOo At 2:20, the ...
0
votes
0answers
8 views

Stable equilibrium position of 3d models.

I have 2 models, described by vertices arrays. The aim is to find stable equilibrium position of one of the models upon the other. The algorithm should consider the possibilities of transformation of ...
0
votes
0answers
21 views

Calculating the length of a NURBS curve

I'm attempting to find the length of a NURBS curve, but I'm not having any luck (I'm also not entirely sure if NURBS are more of a programming thing, I initially asked this question over on Stack ...
0
votes
0answers
30 views

Rotation plane on the sphere (quarternion)

I asked similar question on stackoverflow but still no answers.http://stackoverflow.com/questions/25185329/image-rotation-with-the-gyro-data-math I assume it is more math than programming problem. ...
2
votes
2answers
45 views

Two and Three Variable Limit Questions

Find the following limits, if they exist. $$\lim_{x,y\rightarrow 0,0}\frac{x^2 + \sin^2 y}{\sqrt{x^2+y^2}}$$ I believe we're suppose to use the squeeze theorem on this first one above. Possibly ...
1
vote
1answer
39 views

Intersection of two lines in 3D

The two points $A=(x_{0},y_{0},z_{0})$ and $B=(x_{1},y_{1},z_{1})$ are given. I want to find the coordiantes of the point $C=(x,y,z) $. The line segments $AC$ and $BC$ make equal angle $\alpha$ with ...
1
vote
0answers
37 views

slope of a plane

I'm trying to understand the math behind 3d perspective clipping algorithm dixit: We need four constant to express the equations of the four side planes. These are the slopes of the planes in ...
2
votes
2answers
52 views

Formula to display a $3D$ $90$ degree pipe bend

I am trying to display a $3D$ Pipe with $90°$ bend. I am writing code for it, but I am sure this is more of a mathematical question as a programming one. It would be nice if anyone could help me ...
4
votes
1answer
43 views

Find out whether two rectangles are intersecting in 3D space

I've got two rectangles in 3D space, each given by the coordinates of their 4 corners. They are not axis aligned, meaning their edges are not necessarily parallel/perpendicular to the world axes. Each ...
0
votes
2answers
30 views

Efficiency in vector translation by matrix instead of vector

I try to understand math for 3D games. If I want to translate a point, I may do it in two ways: 1. Using vector summation. 2. Using matrix multiplication. For example: Initial vector $p =(1,2,3)$. ...
0
votes
1answer
21 views

Oblique projection for which the projection vector is at an angle of 45 degrees

dixit: A special case of oblique projection is called cavalier projection. It is given when the projection vector forms an angle of 45° with the z-axis. This means that: $$(x_p^2+y_p^2)/z_p^2=1$$ My ...
1
vote
2answers
50 views

Derive a quaternion from three axis

My problem originates from some code that I'm writing to parse an obscure file-type in which a geometric entity is defined in it's own 'local space', and a rotation and translation are provided to ...
3
votes
1answer
72 views

Making a function periodic

This might not be the best place to ask this question, but here it goes... I'm creating a game and need 3D sea waves. Since it's for mobiles, there's no time to generate entire screen worth of waves ...
0
votes
0answers
47 views

Water swallowing in Matlab

I want to simulate some water passing through a vertical cylinder in Matlab, and I would like to implement a 3d animation of it. I built the cylinder using the patch function, but I do not know how to ...
1
vote
2answers
78 views

To find the center of gravity of a homogeneous tetrahedron

The center of gravity coordinates of a triangle can be calculated $O(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3},\frac{z_1+z_2+z_3}{3})$ where $P_1,P_2, P_3$ are the corner points of a homogeneous ...
1
vote
1answer
40 views

Elevation of 3D function

$f(x,y) = \begin{cases} x^2/y & y \neq 0 \\ 0 & y = 0\end{cases}$ I need to draw the elevation (or you may call it Equivalent curve) of this function and I don't know how to draw them. Can ...
2
votes
0answers
72 views

Rotating a cube about an axis through opposite vertices

I have a cube made using CSS transforms that I'm trying to animate rotating about an axis going through 2 opposite vertices. What I have: Initial cube: ...
0
votes
1answer
22 views

Translation of basis for a vector space on the specified distance

In the Euclidean space $XYZ$ is a basis $X_1Y_1Z_1$ defined that is specified by the vectors $\overrightarrow {O_1X_1}$, $\overrightarrow {O_1Y_1}$ and $\overrightarrow {O_1Z_1}$. How to calculate ...
1
vote
0answers
36 views

Intersection between 2 lines (3D). This doesn't have a solution does it?

so I was looking through an old exam and this question was given: The teachers answer was the point (9, -9, 21) I tried solving this myself, I got x = x, y = y, but I could not find a point where ...
0
votes
1answer
22 views

Why does a 3d line of segments with constant angles always make a helix?

I have a chain of discrete segments, of equal sizes, built by the following rules: 1)every next segment rotates around it's Y axis by 7 degrees, 2)then it pivots at the join with the previous ...