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
3answers
48 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
33 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
62 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
93 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
50 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
520 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
18 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
33 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
74 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
37 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 ...
3
votes
4answers
72 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
68 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
321 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
104 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
48 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
139 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
82 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
44 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 ...
11
votes
4answers
276 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
52 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 ...
0
votes
0answers
81 views

Bin packing 3D / container loading problem : algorithm with “real” constraints handling

I search a bin packing 3D (or container loading) algorithm (for truck load) with handle of many differents constraints (for each item : stackability, possibles orientations, multi customers, max ...
0
votes
0answers
39 views

Find the direction from which the projected area of a loop is maximal

How do I find the direction from which the projected area of a loop is maximum? Should I try to use intuition or is there a simple mathematical way to find it? The problem given was the following: ...
0
votes
0answers
120 views

Equation of 3D arc given 2 points and radius

Aim Let A be the initial position of a sphere "alpha", and B the location of its target somewhere in 3D space. In my application, this target is close to another sphere "beta", and so depending on A ...
0
votes
1answer
189 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 ...
1
vote
2answers
40 views

Reflection of a plane in a plane.

The question is: The reflection of the plane $2x+3y+4z-3=0$ in the plane $x-y+z-3=0$ is the plane: I tried to find the equation of the normal to the plane and then tried putting in some values, but ...
0
votes
0answers
62 views

net of oblique cone,why it has a shape like this?

today i was building a right cone for my geometry homework.after building the cone, i started to think what shape the net of an oblique cone (cones with circular base which the axis does not pass ...
1
vote
1answer
62 views

Correct name for non-unit length 'hessian normal form' 3D plane.

A plane defined as 4 numbers (x,y,z,distance) is known as the hessian normal form, Where the xyz values are unit-length. However I've found its not necessary to ...
1
vote
0answers
16 views

3D topographic progress compensation by the least squares method.

I'm looking for an explanation of the least squares method used in the case of a correction of 3D point network. We have reference points with known coordinates XYZ, we calculate intermediate points ...
0
votes
1answer
61 views

Get circle around line in 3D plane where all points of the circle lie on the lines perpendiculars

Perhaps I didn't use the appropriate terms to describe my question, so I'll try my best to describe it. Imagine a line in a 3D plane. Now imagine a circle forming around it at a certain point, where ...
0
votes
0answers
64 views

How to calculate the critical density estimation for “continuum” percolation model in “3D space” when we have “spatial correlation”?

I want to approximately estimate the critical density (lower bound for density) of balls in a cube to make sure that the upper and lower surfaces of the cube will be connected to each other through ...
0
votes
1answer
24 views

2d indicator for turning a spacecraft in 3d space

For the admins Please look at the tags.... I have no idea where to put this in math I also posted this here http://www.gamedev.net/topic/666267-2d-indicator-for-turning-a-spacecraft-in-3d-space/ ...
0
votes
1answer
43 views

What are the coordinates of your position?

Suppose you start at the origin, move along the x-axis 3 units. Then face downwards and move forward 4 units. Then turn right and move 7 units. Then (relative to your current position) face downwards ...
2
votes
1answer
92 views

Does there exist a harmonic map from S^2 to 3d hyperbolic space

My question is, does there exist a harmonic map from $S^2$ to $\mathbb{H}^3$ , $\mathbb{H}^3$ means the 3d hyperbolic space. In addition, if it exist, could we directly construct the map? Thank you ...
1
vote
2answers
81 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 $\vec{p}$, ...
0
votes
0answers
19 views

Help with a vector transformation on the surface of a sphere

I have a 3D system with an eye looking at a centre of vision (COV), and the eye has an orientation (up) vector. I need help in transforming the up vector as the eye moves around the COV. The eye can ...
0
votes
2answers
263 views

Rotation about an arbitrary axis

I'm dealing with rotation about an arbitrary axis and I know the vector of this axis and angle that I want to rotate. Is there a way to calculate angles of this rotation into a rotation about an XYZ ...
0
votes
0answers
73 views

Projecting point in 3d space onto a 2d view

If I have the following information: The coordinates in 3d space of a point(x, y, z) The dimensions of a 2d viewing window(width, height) The coordinates in 3d space of the center of that view(x, y, ...
0
votes
0answers
28 views

What is the topology where all the direct distances are equal to $d_1$ and all the cross distances are equal to $d_2$

What is the topology (2D or 3D representation) that corresponds to the following description: We have $K$ pairs of points, where pair $k$ is denoted as $(P_k,Q_k)$. We suppose that the distance ...
1
vote
1answer
54 views

Rotate the segment by quaternion - how to find actual segment's end position?

I have an segment from [0,0,0] to [0,1,0] (left-handed coordinate system, with Y axis up) which is non-rotated. The rotation is ...
1
vote
4answers
138 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, ...
1
vote
1answer
67 views

“Octahedron” made from two pyramids of different heights.

I wonder how to name such shape: It's commonly used by e.g. 3ds max to visualize the bone in animation system. It consist of two pyramids with the exact same square base. It would be a ...
0
votes
1answer
224 views

Given a line and a plane determine whether they are parallel, perpendicular or neither

The line $L$ passes through the point $p = (1,-1,1)$ and has direction vector $d = [ 2,3, -1]$. Determine for the plane $P$, with equation $2x+3y-z = 1$ whether $L$ is parallel, perpendicular or ...
2
votes
1answer
85 views

How do I find if a point exists in a3D solid?

I am attempting to write a program in which I must determine if a point with known x, y, z coordinates exists within a solid with 8 vertices. All the dimensions of the vertices are known. In terms of ...
1
vote
0answers
102 views

Trying to find the volume of a 3D torus shape that I made

After playing around with 3D parametric equations on my calculator (modifying the equations of a standard torus), I came across a shape that I like. The equations are: $$x=(2+\sin t)\cos u$$ ...
0
votes
1answer
66 views

Line Segments that end at the same point

Given the starting position and length of two line segments (P0, L0, P1, L2), find the configurations where both segments end at the same point. Both starting points can be anywhere in three ...
0
votes
1answer
52 views

Dot product of two cross products in $\Bbb R^3$ with general metric

I would like to find the generalized formula of the identity $$(A\times B).(C\times D)=(A\cdot C)(B\cdot D)-(A\cdot D)(B\cdot C)$$ which holds in an Euclidian metric, within a general metric $g$ on ...
0
votes
1answer
111 views

How to find rotation quaternion for a model so that it is perpendicular to a line in 3D space?

How to find the target rotation quaternion for a model when one of its faces need to be aligned perpendicular to a line in 3D space. For example, if the model is a cube and if two 3D points connecting ...
0
votes
1answer
86 views

Translate 2D point to 3D coordinate system

I have a bunch of points in a 3D coordinate system that approximates a circle. I'm able to find the best-fitting plane of the points, and then find a 2D coordinate system in that plane, using the ...
0
votes
0answers
173 views

Calculate x,y,z given angles and magnitude of vectors

I am making a program where the user can input their desired velocity as well as pitch, yaw, and roll of an airplane, and then I will animate it. I am accomplishing this by updating it's position by ...
1
vote
3answers
52 views

Find the Range and Domain of the following function

The function is: $f(x,y) = \frac{2}{\sqrt{3-x}} + \frac{1}{\sqrt{4-y}}$ I have found the domain and the Range intuitively. But how would I formally prove that my assumption of the Range and Domain ...