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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1answer
48 views

Find the intersection of two planes.

Find the intersection of the planes $x+(y-1)+z=0$ and $-x+(y+1)-z=0$. These two planes are 3-dimensional and I am confused on how to solve it.
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0answers
40 views

3d transformation in html5

I am trying to understand 3d-transformation in html5 and when it's rotation, scaling and moving - it is simple. But adding perspective confuses me. For example we have a rectangle: [400, 200], origin ...
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1answer
125 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 ...
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1answer
31 views

Equation of a plane containing a point and a line

Find the equation of the plane containing the point (0, 7, -7) and the line $\frac{x+1}{-3} = \frac{y-3}{2} = \frac{z+2}{1}$ I'm not sure how to tackle this question, since the equation of the line ...
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2answers
46 views

How to create a nice sky route

I'm trying to find a nice algorithm to trace a sky route between 2 points of a planet. Here is where I am : https://dl.dropboxusercontent.com/u/17657227/migrationGlobe/index.html (or here ...
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1answer
154 views

Understanding the Equation of a Möbius Strip

I am in HL Math and trying to finish my IA. My topic is the Möbius band. The only problem is, I do not understand the formula that defines it and everywhere I have looked has just given me a ...
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1answer
34 views

Compare 2 coordinate systems in 3D space

How would i demonstrate that 2 coordinate systems are identical (that only a translation differentiate them) in 3D space? Let's say i have a coordinate system X Y Z and a coordinate system x y z.
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3answers
212 views

Eating a cake from the inside.

Imagine that you are in the centre of a cube of cake with a known size. In order to move you must eat the surrounding cake but you can only move within the restraints of the six obvious directions ...
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2answers
854 views

Formula to project a vector onto a plane

I have a reference plane formed by 3 points in R3 – A, B & C. I have a 4th point, D. I would like to project the vector →BD onto the reference plane as well as project vector →BD onto the plane ...
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1answer
28 views

How to compute the *vertical* distance between a point and a triangle in 3D?

The point is either above or under the triangle i.e. if you project the point and the triangle on the ground, the point lies in the triangle. I want the distance DD' (in dark red) on the Z axis of ...
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1answer
75 views

vectors in 3D space and Right-Hand Rule

Suppose we have three vectors in 3D space. My questions are: How we check if these vectors are satisfy the right-hand rule or not. I know that it's possible to make the three vectors satisfy the ...
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1answer
34 views

find a point in 3D space

Suppose we have $3$ fixed points $P_1, P_2, P_3$ in $3$-D space, their coordinates are $(x_i, y_i, z_i)$ for $i=1,2,3$. The problem is to find a point $P$ so that the distances from $P$ to ...
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0answers
85 views

What is the Area formed when a line is traced between two 3D curves?

This question is quite related to intersection of cylinders, Hyperbolic paraboloid and modelling. I am welding a trunnion to a pipe (both are hollow cylinders in different geometry). They intersect ...
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1answer
100 views

Can I define a plane given 2 points in xyz coordinates as well as roll angle about that vector?

I am working on a complex motion analysis, trying to calculate wrist angles in 3 dimensions. I have sensors placed as this diagram depicts and need both flexion/extension angles as well as ...
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1answer
143 views

Unit Vector Based on Angle with XY-YZ-XZ Planes

this may be a simple one but lets assume I have 3 angles (a,b,c) and I want to know what unit vector makes such angles with the XY-YZ-XZ planes. Another question is that I wanna know if a,b and c are ...
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1answer
415 views

Finding Rotation Axis and Angle to Align Two “Oriented Vectors”

In general, one can align a 3D vector $\vec A$ to another 3D vector $\vec B$ by rotating $\vec A$ around the axis $\| \vec A \times \vec B \|$ by the angle $\arccos{(\| \vec A \| \cdot \| \vec B ...
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0answers
63 views

How to calculate center coordinates of two reverse arcs in 3D space

Given 3D points P1(200,60,140), P2(300,120,110), P3(3,0,-1), P4(-100,0,-1) and the radius of arc C1MP3 is equal to radius of arc C2MP1. How do I calculate coordinates x, y, z of points C1 and C2? ...
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0answers
21 views

The exact type of my 3d model

I have reconstructed vertical features (hole like objects lie on a vertical face) lie on two connected faces. To understand the situation, I say I have 2 walls with many windows and doors on ...
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1answer
52 views

Perspective projection onto y/z plane?

On wikipedia there is an article on 3d perspective projection onto the x/y plane. http://en.wikipedia.org/wiki/3D_projection#Perspective_projection How do I project onto the y/z plane? If i have a ...
2
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2answers
65 views

Height at 2D coordinate on a 3D rectangular surface

The Problem: How can I obtain every 3D coordinate on a rectangular surface given x and z? For those who are visual, picture looking down on the surface, and finding the height at where the x and z ...
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1answer
41 views

Most appropriate statistics for position error in 3D space.

I have some data on location in 3D space, and am analyzing a couple of models that are supposed to predict the said location. The data I have is a collection of distances as a function of time ...
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1answer
130 views

Find Equation of a Perpendicular Line Going Through a Point

I have the following parametric equation for line g: $$ x=3t\land y=-7+5t\land z=2+2t $$ I have to find the equation of a line perpendicular to $g$ and going through point $Q(3,-2,4)$ which lies on ...
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1answer
22 views

Normal to a 3 Dimensional line

So I have a 3D line: (0,0,0)+t(3,4,7) and I'm trying to find the normal of this. I know the gradient of the normal would normally be -1/gradient but I'm not sure how you would find the gradient with ...
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0answers
41 views

Euler rotation and manipulation of one angle

I've got an acceleration in a certain orientation (which I call local orientation). I known the Euler angles with respect to the global orientation (stored in orientation matrix). Calculating the ...
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3answers
44 views

rotations in 3d space

When looking at rotations in 3d space, does specifying two points (say point A is rotated to point B) determine the whole rotation, or is there a degree of freedom left?
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1answer
90 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 ...
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1answer
42 views

Which of these rotation matrices represents a positive rotation in three-space about the y-axis?

This is what Wikipedia says: \begin{bmatrix} \cos \theta & 0 & \sin \theta \\ 0 & 1 & 0 \\ -\sin \theta & 0 & \cos \theta \\ \end{bmatrix} This is what I think it should ...
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2answers
50 views

Formal definition of plane

The formal definition of plane says that: A plane is a set of points such that if any two points are taken on it, all the points lying on the line joining these two points also lie on the plane. The ...
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2answers
121 views

Identifiying the next point on the surface of a cube ( or 3D object )

I have a cube of unit length. Each face of the cube is divided into 10 x 10 equal segments. Consider an object of size equal to that of a segment moving through the surface of the cube ( or any 3D ...
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0answers
34 views

Finding point of contact of a sphere in an image

I have an image, in which there is a table, and on this table, a sphere. I would like to find the point of contact between the sphere and the table. This point can be the center of the sphere, for ...
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0answers
44 views

Noob Question about a discrete surface

I am looking for a nudge in the right direction as to how to solve this problem. I have data which defines a solid cylinder. The data is composed of a 3d internal radius and a thickness at each point ...
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1answer
112 views

How do i prove the formula for the volume of a cone? [duplicate]

I need a general proof for any form of a cone, not a right circular one.
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2answers
105 views

Minimum distance between point and face

Given a point in 3D space of the form (x, y, z) and a triangle consisting of 3 vectors (also in the (x, y, z) format), how would I calculate the minimum distance between the point and the face of the ...
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3answers
125 views

Which solids are characterized by their orthographic projections?

If I know the orthographic projections of a given solid in Euclidean 3-space onto the $xy$, $xz$ and $yz$ planes, under which circumstances can I reconstruct the solid based on that information alone? ...
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1answer
54 views

Creating rectangle on 3D plane

I would like to create a rectangle from two given 3D points (they are placed on rectangle diagonal). Those points lies on the same plane with given normal. I was able to do it on axis aligned planes, ...
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1answer
44 views

Computing the gradient in a discrete $\mathbb{R}^3$ without a function : is this correct?

Given a $3$D mesh, which is nothing more than a set of points with coordinates on the $3$axis, I follow the intuitive definition of gradient, which means I'm trying to get the "slope". Following ...
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0answers
43 views

Finding area of intersection between 2 circles projected on a 3D mesh

disclaimer: I'm using terms from the 3D modeling world, so a "mesh" is just a finite set of 3D vertices, edges and polygonal faces; and with "topology" I mean the way the given mesh appears to the ...
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1answer
26 views

Finding coordinates on line in 3d environment, given origin and direction

Working on a 3d game, I've encountered a math problem that gaming/stackoverflow hasn't been able to help with. Given an origin coordinate x,y,z, and a yaw/pitch direction away, how can I properly ...
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0answers
37 views

Generating a 3d ribbon from a series of points

I am attempting to generate a 3d ribbon from a set of 3d points. The idea is to generate a realistic ribbon which follows those points. In its current state, one example looks like this: In this ...
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2answers
1k views

How to calculate interpolating splines in 3D space?

I'm trying to model a smooth path between several control points in three dimensions, the problem is that there doesn't appear to be an explanation on how to use splines to achieve this. Are splines a ...
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2answers
89 views

Finding a point on a 3d line

I have two points in 3D which will create a single ray. I am trying to find a point on that ray which intersects a plane who's y coordinate is 0. So how do I find a point on a 3D line when I know the ...
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2answers
105 views

Getting angles for rotating $3$D vector to point in direction of another $3$D vector

I've been trying to solve this in Mathematica for $2$ hours, but got the wrong result. I have a vector, in my case $\{0, 0, -1\}$. I want a function that, given a different vector, gives me angles DX ...
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votes
1answer
120 views

Find rotation matrix of vector rotated around a point

Given a unit vector $a$ and a point $(x,y,z)$ if I rotate $a$ around $(x,y,z)$ I get the vector $b$. My question is, given $a$, $b$ and $(x,y,z)$ can I recover the rotation matrix used to rotate $a$ ...
0
votes
1answer
210 views

distance between parametric line and a point (4,3,s)

I've tried solving this problem every way I know how and I just can't get it. I've looked at similar problems of this type, and I still cannot get an answer that seems right. Parametric Equations: ...
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1answer
56 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 ...
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0answers
63 views

Least Squares Conformal Map Algorithm for UV coordinates

Can someone explain Least Squares Conformal Map in terms using Vertices(Vx,Vy,Vz) and UV coordinates or ST coordinate? I have read the lscm paper but I need it in XYZ value to understand it. ...
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0answers
116 views

how to calculate the volume of irregular shape by the Cartesian coordinates of its corners?

I've 4 points in a plane "A" and another 4 in another plane "B". is there a way to automatically calculate the volume contained into this irregular box? The automation is important as this set of 8 ...
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1answer
111 views

Direction Cosines and Rotation Angles

I'm rotating an object in 3D space with respect to a relative base, or reference frame. I'm using a normal vector to represent the rotation angles. Suppose you have an object parallel to the ...
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2answers
262 views

What are the coordinates of the vertices of a regular tetrahedron, relative to its centroid?

I am trying to draw an equilateral/regular tetrahedron in Processing (subset of Java), so I have to define 4 triangles that meet at the 4 vertices. I have been able to find the coordinates for the ...
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0answers
43 views

determine the position of axis in 3d space

I added a picture here for the challenge of the day! I have a coordinate system (Xg, Yg, Zg) marked in blue color, and I want to determine their positions in the space (Xf, Yf, Zf). Those are unit ...