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
45 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 ...
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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
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2answers
58 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
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1answer
44 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 ...
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2answers
31 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 $p =(1,2,3)$. ...
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1answer
24 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 ...
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2answers
53 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
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1answer
77 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
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0answers
53 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
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2answers
86 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
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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
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0answers
80 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
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1answer
24 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
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0answers
37 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
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1answer
26 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 ...
1
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1answer
59 views

Software to easily draw 3d plots from functions

my problem is that I need a way to quickly check results of my, that is to say, homework. I think that the best way to do this is to draw a plot of a function to quickly see whether my solution is ...
1
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2answers
62 views

Area of projection of cube in $\mathbb{Z}^3$ onto a hyperplane

A cube with vertices $(\pm 1, \pm 1, \pm 1)$ gets projected into the plane perpendicular to vector $\mathbf{n}\in S^2$. The projection is a hexagon, how do I find the area? I think I can just ...
1
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1answer
68 views

To find the volume of the region that is bordered by 4 points in 3D space

To find the volume of the region that in the points $A(x_1,y_1,z_1),B(x_2,y_2,z_2),C(x_3,y_3,z_3),D(x_0,y_0,z_0)$. Let's define a 4X4 matrix to determine plane equation that are on $A,B,C$ ...
0
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2answers
70 views

Parametric equation for intersection of curve

Here's the three part question: A) Find parametric equations for curve which is the intersection of the cylinder $x^2 + z^2 = 1$ and the plane y = -x. B) Show that the curve lies on the surface $x^2 ...
6
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1answer
77 views

Probability that two circles in space are linked

Let $C_0$ be a circle centered on the origin, and $C_1$ a circle centered on $(1,0,0)$, center distance of $1$. Q1. If both $C_0$ and $C_1$ are randomly oriented and have the same radius $r ...
0
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1answer
21 views

What is and what are the use for an “ AINV preconditioner ” or “ SAINV ”?

In an article that I'm reading there is a mention to this "thing" and I absolutely don't know anything about it, for me it could be anything. I noticed that this thing is somehow related to the math ...
0
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0answers
22 views

Rotation of point with infinite child objects. (Chain rotation)

More of a thought experiment here, knowledge for knowledges sake. Let's say you can create infinite points that rotate smoothly and at the same speed as each other through a full revolution - let's ...
2
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2answers
64 views

Finding a 3rd coordinate of the rectangle points in 3d

I have a 4 3-D-points, each of them has only 2 of 3 known coordinates, as follow (? is unknown here): P5 (P5x, P5y?, P5z) P6 (P6x, P6y?, P6z) P3 (P3x, P3y, P3z?) P4 (P4x, P4y, P4z?) They build ...
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1answer
39 views

Volume of Cavity between intersecting multiple Spheres

I want find an equation for this problem: Problem Statement:: I have different size sphere, for example say $R_1$ for Red balls and $R_{2}$ for white Balls, overlapping each other. 1.) I want to ...
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3answers
46 views

What 3D graph does $x^2+2z^2=1$ give?

I am missing the 3D graph for the equation $x^2+2z^2=1$.
0
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1answer
21 views

Calculate position of N points around given point in 3d space?

Sorry if I used wrong words - English is not my native language, and I never actually studied geometry. For a project I'm working on, I need to calculate set of points, that: are in given, ...
0
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0answers
55 views

Angular displacement/speed of a rotating sphere from 3d points

I have 3d points on the surface of a unit sphere that describe every minute its rotation. I want to know angular velocity of this sphere. The sphere center is fixed and the axis of rotation can change ...
2
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1answer
37 views

Creating a surface from a path of 3D cubic bezier curves

I have a list of cubic bezier curves in 3D, such that the curves are connected to each other and closes a cycle. I am looking for a way to create a surface from the bezier curves. Eventually i want ...
0
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1answer
42 views

transform line and point in 3d and 2d space [closed]

I have a line which is described with two point and I know (x0,y0,z0) and (x1,y1,z1). After that I transform it to 2d space dividing with -z0 and -z1 values. Problem is that if I know (a,b) how can ...
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0answers
25 views

Seams/net of curved surfaces

Like with the seams of a piece of clothing or inflatable, what would the methodology be to creating a flat net of a curved 3d object? I would like to create a model of a mobius torus, and would like ...
5
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1answer
77 views

Find all such functions defined on the space

$f:\mathbb{R}^3\to \mathbb{R}^{\ast}$ is such that for any non-degenerate tetrahedron $ABCD$ with $O$ the center of the inscribed sphere, we have : $$f(O)=f(A)f(B)f(C)f(D) $$ Prove that $f(X)=1$ for ...
0
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1answer
49 views

How can I transform a 3D triangle to xy plane

Suppose I am given a triangle ABC and its corresponding vertex coordinates in 3D. I want to transform ABC in such a way so that vertex A lies on global (0,0,0) coordinate, B lies on (dist, 0, 0) ...
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0answers
60 views

Proving the 3-d pythagorean theorem on surface areas of oblique triangular pyramid

I would like suggestions if possible, other than the really sloppy picture, I'll edit that once my dad gets me Microsoft office. I got a snip of the shape, and edited it as best as I could. The ...
0
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0answers
113 views

How to average 3D Scale Vector?

I'm working in a 3D application and I'm trying to average scale values together, but I'm missing a step. The x, y, z scale values in my problem will all be the same so even though my values will be ...
0
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1answer
34 views

Given a point origin, find ray that intersects two lines

I'm working on a specific shadow calculation for a graphics project. I have a point light source obscured by a straight edge object, and I want to find where the edge of the shadow intersects a ...
0
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1answer
71 views

Triangle in 3D space point X and Y coordinate know find Z

I have a triangle in a 3D space. I know the points X an Y coordinate but I dont know the Z. How can the Z be calculated by knowing the points of the triangle and the X an Y coordinate of the point ...
2
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2answers
66 views

Calculate coordinate of any point on triangle in 3D plane

I am really stuck and can't find right way to write a formula(s) that will calculate Z coordinate of point on triangle plane in 3D plane. I know all coordinates of triangle points ( Ax, Ay, Az, Bx, ...
-1
votes
1answer
43 views

Finding how “spreaded” a point cloud in 3D

I don't know the proper term for "spreaded" but what I want to find is, a value that indicates how far is an average point from the centroid. I think this is standard deviation of the point set, but ...
1
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2answers
82 views

Rotate XYZ frame in 3D space

Given a XYZ frame in 3D space at origin O(0,0,0). And given a plane equation: ...
0
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1answer
23 views

Area of triangle on a sphere (not spherical triangle)

How do I find the area of a triangle on a sphere, and the triangle is not a spherical triangle, for example, the triangle is formed with two geodesics and a line of latitude. Is there a specific ...
1
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1answer
25 views

Given an axis of rotation and an angle, work out the rotation angles around x,y,z axis

I want to convert from one 3D rotation convention to another. The first convention has an axis of rotation, $\boldsymbol{r}$ and an angle $\theta_r$ to rotate about this axis. The second convention ...
0
votes
1answer
50 views

x(u,v), y(u,v), z(u,v) parametric equations for a special cycloid

I'm trying to find out a 3d parametric equations for a cycloid I know that a cycloid is a 2d curve it is generated by a point on a rolling circle. but my circle is rolling around another circle both ...
0
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1answer
39 views

Euler angles for mapping three points on a sphere to three other

Let $\mathbf{a}$, $\mathbf{b}$, $\mathbf{c}$ be points on the unitary sphere, so that $\|\mathbf{a}\| = \| \mathbf{b} \| = \| \mathbf{c} \| = 1$. Let $\mathbf{a'}$, $\mathbf{b'}$, $\mathbf{c'}$ be ...
0
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2answers
56 views

Collision detection between two accelerating spheres with no initial velocity?

We have two non-touching spheres of radii r1 & r2 are lying in space at rest. Both of them are then given accelerations a1 & a2 respectively at time t=0. Find whether they will ever come in ...
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0answers
26 views

Mapping between two unknown 3D coordinate systems from common motion

Coordinate systems A and B are rigidly linked in an unknown way. The platform then moves and the motion vectors [RA|TA] and [RB|TB] are calculated in each coordinate system. They are parallel but not ...
0
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2answers
88 views

Difference between Euclidean space and vector space?

I often hear them used interchangeably ... they are very complicated to make any use of. Wikipedia words: Euclidean space: One way to think of the Euclidean plane is as a set of points ...
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0answers
25 views

Famous graphs with nice 3D embeddings

The Petersen graph has an interesting 3D embedding. Take a tetrahedron. Add a midpoint to each edge. Connect opposing midpoints for a Petersen graph. The Perkel graph or 57-cell has an interesting ...
1
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0answers
16 views

rotating vector based on plane normal

This is probably very basic, but here is a drawing of what I'm trying to achieve : Explanation : Those are 3D normalized vectors and I'm trying to change v1 to v1' based on vn. As shown in the ...
2
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0answers
25 views

Volume of overlap between two convex polyhedra

I have two convex polyhedra represented by triangle meshes. I can easily determine if they are in contact or not, but when they are in contact then I would like to determine the volume of their ...
0
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1answer
22 views

Incorporating an error ellipse from eigenvalue/vectors into 3D geometry

I have a 3D point with a covariance matrix, and an associated 3D vector that begins at the point. I would like to be able to consider alternative points for the starting position of the vector, ...