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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45 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: ...
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0answers
55 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 ...
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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 ...
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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
30 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
34 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
49 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
33 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
70 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 ...
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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 $\vec{p}$, ...
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0answers
8 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 ...
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2answers
73 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 ...
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0answers
32 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, ...
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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 ...
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1answer
23 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 ...
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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, ...
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1answer
42 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 ...
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1answer
57 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 ...
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1answer
37 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 ...
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0answers
57 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: $$x=(2+\sin t)\cos u$$ ...
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1answer
24 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 ...
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1answer
37 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 ...
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1answer
28 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 ...
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1answer
44 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 ...
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0answers
58 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 ...
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3answers
47 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 ...
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1answer
23 views

How do you determine if two triangles are intersecting for collision detection?

I've been scouring the internet for things about intersecting triangles. I haven't been able to find something that just gives me the math and what all the variables are equal to. I would love the ...
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1answer
14 views

distances measured in space

how do we find the distance of a point from a given line measured parallel to a given plane? Here is a a sample question : find a distance of point (2, 3, 4) from line (x+3)/3=(y-2)/6=z/2 measured ...
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1answer
43 views

Change angle of a vector to another vector

Let $\mathbf{x},\mathbf{y},\mathbf{w}$ be the following 3-vectors: $$\mathbf{x}=\begin{pmatrix}x_{1}\\ x_{2}\\ x_{3}\end{pmatrix}\qquad\mathbf{y}=\begin{pmatrix}y_{1}\\ y_{2}\\ ...
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2answers
70 views

Plane that passes through the point (−3, 2, 1) and contains the line of intersection of the planes x + y − z = 4 and 4x − y + 5z = 2

Find an equation of the plane. The plane that passes through the point (−3, 2, 1) and contains the line of intersection of the planes x + y − z = 4 4x − y + 5z = 2 I know the normal to plane 1 is ...
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2answers
56 views

Finding Equation of a Plane through the origin and the points$ (1, −2, 5)$ and $(8, 3, 2)$

Find an equation of the plane. The plane through the origin and the points $(1, −2, 5)$ and $(8, 3, 2)$ I know $AB$ is $<7,5,-3>$ but I don't know what to do after that
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2answers
71 views

What's the “easiest” closed 3-manifold with a nonabelian fundamental group?

I'm looking for some easy compact, oriented 3-manifolds without boundary that have a nonabelian fundamental group. It needn't be perfect. "Easy" means that it has an easy Heegard diagram, say, one ...
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1answer
18 views

Which of the surfaces does the vector lie on?

So I used the trig identity (y^2 + z^2 = 1) on my y and z component. So I concluded that the cylinder y^2 + z^2 = 4 satisfies the question. I also concluded that the plane x + y = 3 satisfies the ...
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0answers
40 views

Catenary equation in 3D

I have two points with coordinates A(x1,y1,z1) and B(x2,y2,z2). There is a third point which is lowest point of the catenary curve. I only know z-coordinate of this third point. I need to find ...
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1answer
152 views

Equation of a parabola in 3D space

I have two points with coordinates A(x1,y1,z1) and B(x2,y2,z2). There is a third point which is vertex(lowest point) of the parabola. I only know z-coordinate of this point. I need to find coordinates ...
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1answer
41 views

Creating a 3D Plane using the normal and point vector

I'm not understanding the relationship of a normal vector and a position vector that makes it into a 3D plane, and how I can visualize what that 3D plane is going to look like in 3D space. Say I ...
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1answer
33 views

Describing the shape of a level surface given functions

(1) Describe the level surfaces of $f(x,y,z) = sin(2x+y-z)$. For what values of 'c' do level surfaces exist? For this one I set the function equal to c and tried to put it in a more manageable form. ...
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2answers
20 views

Find an equation of a plane

Find an equation of a plane which contains the points: $(0,0,3),(3,2,1)0$, and $(6,2,0)$ I know I need a vector in order to use the equation $d=ax_0$+b$y_0$+c$z_0$ Now, could I just select any two ...
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2answers
16 views

Give parametric equations for the line in 3 space

Give parametric equations for the line in 3 space which goes through the point (1,2,3) and is parallel to the line given by the symmetric equations: (x-1)/-1 = (y-2)/3 = (z-2)/1 So, based off those ...
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3answers
39 views

Parametrization of the intersection of two given surfaces

Find a parametrization of the intersection between the two curves $z=x^2-y^2$ and $z=x^2+xy-1$. I figure I should set them equal to each other but I'm not sure where to go from there: $$x^2-y^2 = ...
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0answers
49 views

Calculating Normals across a sphere with a wave-like vertex shader

This is a bit of a CS question, but more than not it's a 3D math problem. I've been trying to get the correct normals for a sphere I'm messing with using a vertex shader. The algorithm can be boiled ...
2
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1answer
38 views

Finding the unit normal vector

Q. Consider the following vector function. $$ r(t)= \langle 6\sqrt{2}t,e^{6t},e^{-6t} \rangle $$ Find the unit tangent and unit normal vectors T(t) and N(t). I found $$T(t)= ...
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0answers
43 views

Is $y=5 $ a plane in $\Bbb{R}^3$?

I suppose it depends on how you define the variance on $x$ and $z$, but this question seems simple to me: yes. If $P(x,y,z)$ is the set of all points $x, y, z$ such that $y=5$, it seems clear that ...
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0answers
15 views

Randomly distribute objects over a surface with some clusters

I want to randomly distribute some(in thousands) objects over a surface. This I can achieve with a function say x,y = rand(). This will evenly distribute objects over the surface, but is it possible ...
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1answer
167 views

What is the line of greatest slope on a plane? [closed]

Let $P$ be a plane in $\mathbb{R}^3$ that is inclined (neither horizontal nor vertical). When considering lines lying on $P$, it is sometimes said "$L$ is a line of greatest slope of $P$". What is ...
2
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0answers
41 views

Rotate a 3D Vector onto Another 3D Vector

I am trying to transform one triangle onto another triangle in 3D space (Right Triangles). My thought was I align the forward and left vectors, then translate the center of one to the other. ...