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
34 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 ...
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 ...
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
14 views

Cone with 3 mutually perpendicular generators [on hold]

what is general equation of cone touching coordinate planes and please show it diagrammatically
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
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 ...
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 ...
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 ...
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 ...
-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 ...
4
votes
2answers
59 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
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
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 ...
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
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 ...
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 ...
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 ...
-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 ...
0
votes
2answers
39 views

How to find the vector equation of a plane given the scalar equation? [closed]

How would I find the vector equation of the plane: $x + 2y + 7z - 3 = 0$ So far, I found the normal vector: it's $(1, 2, 7)$.
0
votes
1answer
15 views

Extending (projecting) a line in $3D$ space

So I have two points in 3D space, lets call them $p_1=(2,1,-1)$ and $p_2=(3,2,-2)\ $. This is all the information I have about these points. If I wish to extend this line to a $p_3$, how would I do ...
0
votes
1answer
31 views

Perpendicular Lines.

If two lines $L_1$ and $L_2$ in space, are defined by: $$L_1=\{x=\sqrt{\lambda}y+(\sqrt{\lambda}-1)\\z=(\sqrt{\lambda}-1)y+\sqrt{\lambda}\}\text{ and ...
-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 ...
0
votes
0answers
30 views

Rotational matrices

I apologize ahead of time that math isn't my strong suit, I understand most the basic concepts but lots of gaps. So forgive me if i miss use a concept. So I am working in a 3d engine integrating a ...
2
votes
4answers
59 views

Algorithm to generate a hill

Setup I recently started to work with Unity. I want to generate a custom terrain at runtime. To do this i take a grid with a variable amount of squares. For each of the squares i calculate the height ...
0
votes
0answers
48 views

Find the UV distance from a point on a plane with any normal

I have a plane defined by a point(p1) on the plane and its normal (n). I have calculated the point of intersection for another point (p2) by http://geomalgorithms.com/a04-_planes.html. These two ...
0
votes
1answer
274 views

How do you find the cross sectional area of a Tetrahedron?

How is vector's related to this question? If so, how can you use the vectors? I understand that its a triangular pyramid. But how can you show the cross sectional area for any generalised height? ...
1
vote
0answers
25 views

Mapping A point from one 3D Coordinate System to Another 3D coordinate System with Euler Angles between the two systems given

Suppose I have a point in the green coordinate system, and I wish to describe it in reference to the orange coordinate system. I know the roll, pitch, and yaw of the green system with respect to the ...
0
votes
1answer
34 views

Equation of plane parallel to a vector and containing two given points

I'm not sure how to solve this. I started by finding the equation of the line AB.
1
vote
2answers
47 views

How to get projection of ellipsoid onto sphere

I'm trying to get the projection of an ellipsoid onto a sphere. Depicted in the image below, I need the projection of the red ellipsoid onto the unit sphere at the origin. I have tried various ...
1
vote
1answer
39 views

How can I move a point along a line in 3D space to reach a target dot product with a fixed reference point?

Suppose a point in 3D space, Q. For any other point x in that space, Let Q(x) be the unit vector pointing from x towards Q. I also have a line L in 3D space, and a point on this line P. L = {P + ...
0
votes
1answer
27 views

coordinates of 3rd point (vertex) of a right triangle knowing lengths and direction

In a last post I wanted to know the 3rd point of vertex, actually I have some similar problem .... I think I have all data.. for example...: 3 vertex cordinates in order to have the direction(gray ...
10
votes
4answers
219 views

Tricky 3d geometry problem

We have a cube with edge length $L$, now rotate it around its major diagonal (a complete turn, that is to say, the angle is 360 degrees), which object are we gonna get? Astoundingly the answer is D. ...
0
votes
0answers
17 views

Formula for the base edges of a rotated cone

I need to create a set of equations to find points along the edge of the base of a cone, but I'm stuck What I have: The cone can be rotated over any plane in $\mathbb{R}^3$. The position of the ...