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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5
votes
2answers
688 views

Tranforming 2D outline into 3D plane

I am writing a program where I would like to allow the user to draw 4 connecting lines, such as: And convert this shape into a 3D plane. Is this possible? Is there an existing algorithm to do so? ...
5
votes
4answers
3k views

Can the Surface Area of a Sphere be found without using Integration?

When we were in school they told us that the Surface Area of a sphere = $4\pi r^2$ Now, when I try to derive it using only high school level mathematics, I am unable to do so. Please help.
13
votes
8answers
18k views

Calculate Rotation Matrix to align Vector A to Vector B in 3d?

I have one triangle in 3d space that I am tracking in a simulation. Between time steps I have the the previous normal of the triangle and the current normal of the triangle along with both the current ...
11
votes
5answers
14k views

Parametric Equation of a Circle in 3D Space?

So, my dilemma here is... I have an axis. This axis is given to me in the format of the slope of the axis in the x,y and z axes. I need to come up with a parametric equation of a circle. This circle ...
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 ...
2
votes
1answer
87 views

Texture mapping from a camera image (knowing the camera pose)

I'm not sure if I should ask this question here or on stackoverflow, so forgive me if I'm wrong. I want to apply a texture (taken from a camera) on a 3D surface, let me explain my problem: I have ...
0
votes
2answers
7k views

How to find shortest distance between two skew lines in 3D?

If given 2 lines $\alpha$ and $\beta$, that are created by 2 points: A and B 2 plane intersection I want to find shortest distance between them. $$\left\{\begin{array}{c} P_1=x_1X+y_1Y+z_1Z+C=0 ...
5
votes
1answer
75 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 ...
4
votes
1answer
459 views

Automation of 3D Paper Modeling

I recently saw this creative paper contraption online this prior weekend and wanted to see if I could automate the process of creating all ~35 layers of an equation. Essentially what I would want the ...
2
votes
3answers
957 views

3D to 2D rotation matrix

I have been trawling through this forum but am struggling to understand the maths a bit. Currently I have a 2D plane within a 3D space and I have the coordinates for them. I want to work on this 2D ...
1
vote
2answers
114 views

Calculating new vector positions

I'm using the following formula to calculate the new vector positions for each point selected, I loop through each point selected and get the $(X_i,Y_i,Z_i)$ values, I also get the center values of ...
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 ...
0
votes
0answers
147 views

Sample Code to Generate Points on the Rim of a Randomly Rotated Cone : What's Going On Here?

Related to this question: http://math.stackexchange.com/questions/407897/randomly-generate-point-on-shell-from-3-points-2-angles-with-uniform-angle-dis I'm trying to reverse engineer the ...
0
votes
3answers
471 views

Formula for gallons in a trough

I have a trough which is a circular container. How do I determine how many gallons of water it takes to fill up the trough? I was thinking that we measure the height and the width but I think it's a ...
7
votes
2answers
5k views

How to transform a set of 3D vectors into a 2D plane, from a view point of another 3D vector?

I googled around a bit, but usually I found overly-technical explanations, or other, more specific Stackoverflow questions on how 3D computer graphics work. I'm sure I can find enough resources for ...
2
votes
2answers
4k views

How to multiply vector 3 with 4by4 matrix, more precisely position * transformation matrix

All geometry in computer graphics are transformed by position * transform matrix; The issue is the fact that position is a vector with 3 components (x,y,z); And transform matrix is a 4 by 4 with one ...
13
votes
3answers
938 views

Making a convex polyhedron with two sheets of paper

Suppose that we have two sheets of paper $S,T$ and that each of $S,T$ is in the shape of a convex quadrilateral. Also, suppose that the length of the perimeter of $S$ equals that of $T$. (Note that ...
11
votes
7answers
21k 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 ...
5
votes
4answers
2k views

What's the best 3D angular co-ordinate system for working with smartphone apps

This is very much an applied maths question. I'm having trouble with Euler angles in the context of smartphone apps. I've been working with Android, but I would guess that the same problem arises ...
4
votes
1answer
327 views

Uniform distributions on the space of rotations in 3D

I believe on moral grounds that the following three definitions are equivalent, and determine "the" uniform distribution on rotations in three dimensions. The Haar measure on $SO(3)$. The uniform ...
9
votes
4answers
2k views

Find whether two triangles intersect or not in 3D

Given 2 set of points ((x1,y1,z1),(x2,y2,z2),(x3,y3,z3)) and ((p1,q1,r1),(p2,q2,r2),(p3,q3,r3)) each forming a triangle in 3D space. How will you find out whether these triangles intersect or not? ...
5
votes
3answers
765 views

Largest Triangle with Vertices in the Unit Cube

How would one find a triangle, with vertices in or on the unit cube, such that the length of the smallest side is maximized? And what is that length? A lower bound for the length is $\sqrt{2}$, by ...
3
votes
2answers
121 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 ...
2
votes
2answers
41 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, ...
2
votes
3answers
552 views

How to check if point is within a rectangle on a plane in 3d space

Please refer to this image for this question-> I have a 3d bounded box (in green). I also have a 3d line (in red) I know the points a, b, c, d, e. They are points in space with x, y, z, ...
2
votes
2answers
168 views

Is the value of $\pi$ in 2d the same in 3d? [closed]

I am starting with my question with the note "Assume no math skills". Given that, all down votes are welcomed. (At the expense of better understanding of course!) Given my first question: What is ...
1
vote
1answer
93 views

Jacobian of exponential mapping in SO3/SE3

Following this post Jacobian matrix of the Rodrigues' formula (exponential map) What if I really need the Jacobian of the exponential mapping function in $\omega \neq 0$? Basically, I want to ...
6
votes
2answers
398 views

How to divide a $3$ D-sphere in “equivalent” parts?

My goal is to put $n$ points on a sphere in $\mathbb{R}^3$ to divide it in $n$ parts, so that their disposition would be as "equivalent" as possible. I don't exactly know what "equivalent" ...
5
votes
1answer
486 views

Find minimum in a constrained three-variable equation

After my last question I have worked through the math quite a bit and now I'm stuck again. This time my question is less wordy. I have two equations for $t$, one with respect to each $a_{x}$ and ...
4
votes
2answers
625 views

3d transformation two triangles

I have two triangles in 3d. I need to calculate transformation matrix(3X3) between two triangles in 3D. 1)How can I calculate the transformation matrix(rigid) while fixing one of the points to the ...
4
votes
3answers
762 views

Analytically compute signed distance of ellipsoid

I'm trying to generate a 3d signed distance field for a origin centered ellipsoid. For a sphere this is pretty easy: $$\sqrt{x^2 + y^2 + z^2}-r$$ where $r$ is the radius. I'm not sure what the best ...
3
votes
2answers
3k views

How to calculate interpolating splines in 3D space?

I'm trying to model a smooth path between several control points in three dimensions, the problem is that there doesn't appear to be an explanation on how to use splines to achieve this. Are splines a ...
2
votes
2answers
292 views

How to define a perspective circle in xy?

You can see a perspective view of a square(FCED) and a circle in 2D screen. O is center of the circle. How can I define the perspective circle equation that shown as red in the picture? Thanks a ...
2
votes
3answers
934 views

How to show two points in R3 form a plane and determine equation?

Given two arbitrary equidistant points in $R^3$, (p and q), how would one show that they form a plane and what would the equation of that plane be? Defining two vectors in $R^3: (p - 0)$ and $(q - ...
1
vote
1answer
23 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 ...
1
vote
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
vote
1answer
581 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 ...
1
vote
1answer
462 views

How to calculate the direction in which a set of normal vectors (3D) are least oriented?

I have an STL file with thousands of triangular planes with different orientations. What is the best way to calculate the direction in which the normal vectors of the triangles are least aligned? I ...
1
vote
1answer
469 views

Find rotation matrix to match one 3D vector pair onto another

I have two pairs of 3D vectors named $(A_1, B_1)$ and $(A_2, B_2)$. All four vectors have unit length. I'd like to match one pair onto the other. As I am permitted to assume the angle between $A_1$ ...
1
vote
2answers
1k views

Distance Formula in Three Dimensions

The distance formula in 3-D space is defined as: $$|P_1\, P_2| = \sqrt{(x_2- x_1)^2 + (y_2 -y_1)^2 + (z_2- z_1)^2}$$ My question is that if I have 2 points that have negative coordinates, do I have ...
1
vote
1answer
349 views

Closed-form for eigenvectors of rotation matrix

For matrices that are elements of $SO(3)$ is there a formula for the eigenvectors corresponding to the eigenvalue $1$ in terms of the entries of the matrix?
1
vote
2answers
84 views

Normal from multiple vectors

I have a several 3D vectors $X_{i}$ which lay approximately in a plane. Now I need to find a single vector, which is normal (as much as possible) to all of them. For two vectors, I can use a cross ...
1
vote
0answers
333 views

differentiation of polygons, having cross borders

I have point data set and I segmented the data into different planar objects. after that, using contouring (convex hull), I obtained the boundary points. Please assume all points relevant to one ...
1
vote
3answers
5k views

Vector Rotation in 3D

Given: Two points: ($x_1$, $y_1$, $z_1$), ($x_2$, $y_2$, $z_2$) A vector that is parallel to the $x$-axis and points to ascending numbers (intuitively stated, the vector points 'East'). I am ...
1
vote
2answers
772 views

3 Rotations to unit vector (3D)

I've been trying to solve this problem for some time now, but I could really need some help: I have 3 rotations (one per axis) for an object, and want to create a unit vector telling me in which ...
1
vote
1answer
598 views

Find out the border of a planar figure for given a set of points – 2D case

Original post is edited after getting some suggestions; I am looking for a fast algorithm which is able to detect outer most boundary of a plane for given set of points. Suppose, I have 3D point ...
0
votes
2answers
38 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: ...
0
votes
1answer
53 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 ...
0
votes
1answer
345 views

Determine if projection of 3D point onto plane is within a triangle

In 3D, given three points $P_1$, $P_2$, and $P_3$ spanning a non-degenerate triangle $T$. How to determine if the projection of a point $P$ onto the plane of $T$ lies within $T$?
0
votes
1answer
49 views

3d Transformation

I am trying to understand 3d-transformation in html5, but can't understand how we get new (x1, y1) coordinates. For example, we have a plane on our screen with a point at coordinates (287, 431). We ...