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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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 ...
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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 ...
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0answers
34 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 ...
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0answers
17 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 ...
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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 ...
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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 ...
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2answers
34 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 ...
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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
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2answers
56 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 ...
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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 ...
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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 ...
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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 ...
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1answer
25 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
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2answers
23 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 ...
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2answers
49 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 ...
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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", ...
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3answers
40 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
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1answer
22 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 ...
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0answers
13 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
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2answers
175 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
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1answer
43 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 ...
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1answer
46 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 ...
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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 $(1, 2, 7)$.
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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
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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 ...
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2answers
58 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 ...
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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
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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 ...
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0answers
47 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 ...
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1answer
273 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? ...
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0answers
24 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 ...
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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.
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2answers
45 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 ...
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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 + ...
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1answer
26 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 ...
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4answers
216 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. ...
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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 ...
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0answers
44 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 ...
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0answers
28 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
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0answers
52 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
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1answer
125 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
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2answers
33 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 ...
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0answers
28 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 ...
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0answers
34 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 ...
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0answers
10 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 ...
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1answer
33 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 ...
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0answers
48 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 ...
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1answer
14 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/ ...
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1answer
32 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 ...
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1answer
68 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 ...