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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4
votes
2answers
35 views

How to calculate line-line distance when cross product of directions is 0?

I have the lines $$\frac{x-1}{2} = 1-y = \frac{z-2}{3} \tag{1}$$ and $$\frac{x+1}{4} = \frac{4-y}{2} = \frac{z+1}{6} \tag{2}$$ I want to compute the distance between them. I started by putting ...
2
votes
0answers
20 views

Calculate vector of an object aligned to another object in a 3D envorionment

I have an object (100x100x5) with given coordinates and angles. Now I want to place another object aligned to the left/right side of the "original" object. On the X-Axis I need to substract/add 100, ...
-2
votes
1answer
14 views

Determine outer points given more than 2 points [on hold]

Given I have 5 points, how do I determine outer points?
0
votes
3answers
53 views

What does the 2nd degree derivative of a cubic Bezier curve actually represent?

I have a $3D$ Bezier curve. Each co-ordinate along its path is defined by the equation: $$ f(t) = t^3 \bigl(a_2+3(c_1-c_2)-a_1\bigr) + 3t^2 (a_1-2c_1+c_2) + 3t(c_1-a_1) + a_1 $$ where $a_1, a_2$ are ...
1
vote
0answers
14 views

How to compute the best fitting frustum for a set of points?

I am struggling with a problem that I am sure is well known, but I could not find any answer using google or searching on MathOverflow. I have a set of 3D points (x,y,z) and a camera reference frame ...
0
votes
1answer
14 views

what is the difference between an elliptical and circular paraboloid? (3D)

My textbook uses the terms interchangably, and they look the same in graphs, so I was wondering if there a difference between the two? Thanks!
1
vote
2answers
24 views

How to calculate the center of mass for a cloud of 3D spheres?

Given the spheres in 3D space: center(xi,yi,zi), radius and density and the info is stored in an array sphere_data[n][5]: // Sphere_ID x y z radius density 1 x1 y1 z1 rad1 ...
2
votes
1answer
63 views

How can we prove that a three legged chair will never be wobbly?

I am taking the geometry approach. We know from intuition that more than three legs on a chair will make it unstable if any of the legs have a different length than the others. So by "wobble" I mean ...
0
votes
0answers
24 views

Finding position of point (in 3D space ) which are at x,y offset from corner of a rectangle in 3D world

So I am writing a 3D graphic software. And I am stuck at mathematical problem. Mathematically speaking: There's a rectangle (plane) of finite size in 3D space. It can be of any orientation and ...
1
vote
1answer
23 views

Expression of rotation matrix from two vectors

What is the matrix expression of the rotation matrix in 3D which turns a vector $\vec{a}$ into a vector $\vec{b}$, with both vectors given by their coordinates? ($\vec{a} = (a_x, a_y, a_z)$ and ...
0
votes
0answers
14 views

Cone with 3 mutually perpendicular generators [on hold]

what is general equation of cone touching coordinate planes and please show it diagrammatically
0
votes
1answer
26 views

Determining if a point is inside an infinite 3d elliptical tilted cone

I have an infinite 3d elliptical, tilted cone that is defined by a vertex point P(x,y,z) and by 4 angles: the first pair of angles represent the spatial orientation of the cone: θ is the polar angle ...
1
vote
2answers
123 views

Plane intersecting all the lines

This might sound a bit stupid or ill thought, but I am having trouble visualizing it and proving it. Given a finite set $L$ of straight lines in $\mathbb{R^3}$ is it always possible to find a plane ...
0
votes
3answers
2k views

How do I map a 3D triangle into 2D?

The problem I'm having is mapping a 3D triangle into 2 dimensions. I have three points in x,y,z form, and want to map them onto the plane described by the normal of the triangle, such that I end up ...
1
vote
2answers
63 views

Gradient of an angle in terms of the vertices

Let $\theta(\vec p, \vec q, \vec r)$ be the angle theta between 3D real vectors $(\vec{q}-\vec{p})$ and $(\vec{r} - \vec{p})$. What is a simple expression of $\nabla \theta$ in terms of $\vec{p}$, ...
1
vote
0answers
11 views

Calculate the plane angle from 2D plane

I am analysing a squared plane from a perfect cube. This plane is distorted by the perspective view of a camera. I would like to know ask please, some approaches of how could I get to know the ...
0
votes
1answer
18 views

What does this volume represent?

I have been trying to draw this out for an hour now and cannot visualize it. $x$ is between $0$ and $1$, $y$ is between $0$ and $x$, and $z$ is between $x^{2}+y^{2}$. The $z$ line is just a ...
0
votes
0answers
39 views

How to draw regular tetrahedron from center?

How to calculate all four points of regular tetrahedron if you have x,y and z for center point and x, y and z axis rotation and size of tetrahedron? I want to write this in java script and this is ...
0
votes
0answers
19 views

How to construct a surface with a closed curve?

in 3-dimension, suppose that there is a smooth closed curve $C$. Can I say that there is a smooth simply connected(no holes) surface whose boundary is $C$? and is it unique?(I guess not) like ...
0
votes
1answer
17 views

Square surface with four fixed points

I'm looking for a function of two variables, $f(x, y)$, that satisfies the following constraints: $f(0, 0) = z_1$ $f(0, 1) = z_2$ $f(1, 0) = z_3$ $f(1, 1) = z_4$ and within the unit square, it ...
3
votes
4answers
235 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
votes
1answer
334 views

Calculating normals for a polygon mesh (3D computer graphics)

I want to write a program to generate arches, a common architectural form, and export them to a wavefront object format for sharing with various three dimensional graphics editors. To do this, I need ...
0
votes
0answers
8 views

Find the Area of 3d object? [duplicate]

I know I've asked a similar question, but I cannot get the answer. If some 3d object are $(1.2*10^4)$ times bigger than other 3d objects. What is the area of the 3d objects, in square meters, if the ...
-1
votes
0answers
25 views

3D vector perpendicular calculation

Three points $A(6,7,-6)$,$ B(0,0,0)$ and $C(2,6,9)$ are given which are the vertices of a cubes. Find the coordinates of another vertex not on the $ABCD$ plane. I found the answer by finding the ...
0
votes
2answers
42 views

The point A (4, 3, c) is equidistant from the planes P1 and P2. Calculate the two possible values of c

The point $A (4, 3, c)$ is equidistant from the planes $P_1$ and $P_2$. Calculate the two possible values of $c$. Plane $P_1$ has equation $r\cdot (2,-2,1)=1$ Plane $P_2$ has equation $r\cdot ...
3
votes
1answer
407 views

3D Rotation Decomposition?

I have a 3D local xyz coordinate system placed in a world ENU (East-North-Up) coordinate system. The current relationship ...
4
votes
2answers
60 views

How do I find the Intersection of two 3D triangles?

I've got a rather complicated geometry problem that I'm trying to solve - how to find the intersection between two triangles in 3D space. I've looked around at other questions and answers on this site ...
0
votes
1answer
33 views

Three-Dimensional Metrics as Deformations of a Constant Curvature Metric?

I read the following paper Three-Dimensional Metrics as Deformations of a Constant Curvature Metric and discovered the following result: I have three questions: (1) Is $h$ also a conformally flat ...
1
vote
1answer
368 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 ...
6
votes
2answers
177 views

Mystical looking graphs (three-dimensional rotating hearts)

Plop the following into Google: $$ 2-\sqrt{1-x^2-(y-|x|)^2}\cos(30(2-x^2-(y-|x|)^2)),\tag{1}\\ \text{$x$ is from $-1$ to $1$, $y$ is from $-1$ to $1.5$, $z$ is from $1$ to $2$} $$ Here is the result ...
1
vote
3answers
43 views

Geometry - Determine all points along a ray from starting coordinates and direction

I am working on a video game. I need to determine each point along a ray with every x interval with the following information: X, Y, Z coordinates of the starting point of the ray, and, X, Y, Z ...
0
votes
1answer
685 views

How to find line parallel to direction vector and passing through a specific point?

I am give the point $(1,0,-3)$ and the vector $2i-4j+5k$ Find the equation of the line parallel to vector and passing through point $(1,0,-3)$ Could one use the fact that the dot product between the ...
1
vote
6answers
9k views

Find if three points in 3-dimensional space are collinear

Find if the points joining $A=(6,7,1), B=(2,-3,1)$ and $C=(4,-5,0)$ are collinear. How to determine collinearity in three dimensions? In two dimensions, one can compare the slopes of segments ...
0
votes
0answers
16 views

Reflect vector across plane with offset.

I need to mirror an object across a plane in a 3D application. I've been able to do so, however it does not factor in the position of the plane, it only assumes that the plane is at the origin. Here ...
0
votes
1answer
26 views

Calculating plane rotation angles

Let's presume I have an arbitrary plane, for sake of simplification, centered at (0,0,0), described by coordinates of 4 vertices (and normal if needed). Is there any way to describe this plane as ...
2
votes
2answers
24 views

possible polyhedra from euler's formula

I'm not very clear with the euler's formula, and I couldn't find it anywhere. I'm sorry if it is a double post. F + V - E = 2 Is the euler's formula. If the equation balances, is it polyhedra all ...
0
votes
2answers
51 views

Convert a 2D point to 3D on a plane

I have a 2D point and a 3D infinite plane(defined by a 3D point and its normal), I want to convert 2D point to 3D point by projected 2D point onto 3D plane surface. I'm weak in math, I need a method ...
1
vote
4answers
86 views

Best program for 3D plotting

I've hit a roadblock with pgfplots where it has difficulty plotting multiple functions at the same time in 3D. As it states in the manual on page 114, "it cannot combine different \addplot commands, ...
0
votes
0answers
26 views

Can a line in 3-space have all direction cosines $=\frac{1}{2}$

I immediately found that it is impossible since the squares of the direction cosines have to add to 1 and $3 \times (\frac{1}{2})^2 \neq 1$. However, the textbook asks to "interpret geometrically", ...
4
votes
3answers
41 views

Three dimensional rotation of equations.

I have a set of equations that describe a wire in (100) direction. I want to rotate the wire such that it's in the direction (111). My initial plan (which failed) was to use Euler coordinates and ...
0
votes
1answer
338 views

How do you get 3D gradient direction and magnitude?

I know that we can get the magnitude and direction from 2D gradient ? 1) mag(Gx,Gy) = sqrt ( Gx^2 + Gy^2 ) 2) angle(Gx, Gy) = tan^-1 (Gy/Gx) What about in ...
2
votes
1answer
362 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 ...
0
votes
1answer
23 views

What function can produce a perfect saddleback plot and fulfil the following requirement?

I need to find a function that produce a good saddleback plot. The function has the following requirements: Having 2 arguments: x and y Both x and y are natural numbers The result of the function ...
1
vote
0answers
14 views

How do I calculate 3D movement based on yaw, pitch and roll?

I'm creating a 3D game demo and I need to calculate the position of the player in the space (i.e. the player's x, y and z coordinates). I understand that this would be affected based on the camera ...
2
votes
1answer
45 views

Normal of a coons patch at a given point

Disclamer: Rendering the Coons patch is part of 3D Graphics homework, but finding the normals at a given point isn't. Just curious. Here's what I got so far: It's a Coons patch defined by four ...
0
votes
1answer
577 views

Equation of plane through intersection of planes and parallel to line

Find the equation of the plane through the intersection of the planes of $x-2y+z=1$ and $2x+y+z=8$ and parallel to the line: $\frac{x-3}{1} = \frac{y-1}{2} = \frac{z-2}{1} $ I'm facing difficulties ...
-2
votes
2answers
59 views

Volume and surface area of a drilled out cube (BM01 2010/11 Contest Question 2)

Let $s$ be an integer greater than $6$. A solid cube of side $s$ has a square hole of side $x < 6$ drilled directly through from one face to the opposite face (so the drill removes a cuboid). The ...
-1
votes
1answer
47 views

3-Dimentional array

I'm good in 2-D array which is the regular array that has rows and columns, but I have to deal with the 3D array and I can't imagine it, I tried searching for it but with no clue. Any big example of ...
1
vote
0answers
52 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 ...
0
votes
1answer
128 views

Rotate object around a fixed coordinate axis

I am trying to let the user of my app rotate a 3D object drawn in the center of the screen by dragging their finger on screen. A horizontal movement on screen means rotation around a fixed Y axis, and ...