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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8
votes
3answers
224 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 ...
3
votes
2answers
2k 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 ...
0
votes
1answer
41 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 ...
0
votes
1answer
87 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 ...
0
votes
1answer
40 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 ...
2
votes
0answers
92 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 ...
1
vote
1answer
150 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 ...
0
votes
1answer
162 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 ...
1
vote
1answer
648 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 ...
1
vote
0answers
84 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? ...
2
votes
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 ...
0
votes
1answer
75 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
votes
2answers
75 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 ...
1
vote
1answer
44 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 ...
0
votes
1answer
345 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 ...
0
votes
1answer
24 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 ...
0
votes
0answers
46 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 ...
2
votes
3answers
45 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?
0
votes
1answer
143 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 ...
0
votes
1answer
56 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 ...
0
votes
2answers
58 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 ...
-1
votes
2answers
127 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 ...
2
votes
0answers
47 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 ...
1
vote
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 ...
-2
votes
1answer
171 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.
0
votes
2answers
244 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 ...
5
votes
3answers
135 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? ...
0
votes
1answer
85 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, ...
0
votes
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 ...
0
votes
1answer
31 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 ...
5
votes
0answers
42 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 ...
3
votes
2answers
2k 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 ...
1
vote
2answers
156 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 ...
2
votes
2answers
126 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 ...
0
votes
1answer
143 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
411 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: ...
0
votes
1answer
112 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 ...
1
vote
0answers
78 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. ...
2
votes
0answers
142 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 ...
0
votes
1answer
168 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 ...
1
vote
2answers
538 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 ...
1
vote
0answers
44 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 ...
0
votes
2answers
178 views

Find Rotation Matrix to rotate axes and move coordinates of point from P0 to P1

I have a point $P_0 = [x_0, y_0, z_0]'$. I want to rotate the axes so that the new coordinates will be $P_1 = [x_1, y_1, z_1]'$. Define the following rotation matrices: $R_x = \left[\matrix{ ...
1
vote
1answer
50 views

Geometric interpretation of plane

What is the geometric interpretation (coincidence/parallel/intersection) of plane equations, x-2y+z=-1, 2x+y-3z=3, x+8y-9z=9 ?
2
votes
0answers
55 views

Find an SO(3) matrix which satisfies some linear constraints

I have the following optimization problem: $\displaystyle \min_R \sum_{i=1}^n (X_i^T R Y_i)^2$ where $R \in \text{SO}(3)$, i.e. is a 3x3 rotation matrix, and $X_i,Y_i \in \mathbb{R}^3$. If $n \le ...
0
votes
0answers
33 views

Finding the coordinates of the top and bottom circles of a moving and rotating cylinder in 3D

I have a cylinder that is moving and rotating in a 3D space. I need to calculate the coordinates of the center of the cylinder's top and bottom circles. Here's the information I have : I have at the ...
1
vote
1answer
60 views

Determine if a point is contained in the circle in 3d space

I have a problem where I need to determine if a point is contained in the area of a circle in 3d space. For my circle, I have the radius (R), the position of the center (C) and a normal vector to the ...
1
vote
0answers
36 views

Equation of ellipsoid given foci and two semi-axes

How does one find the equation of an ellipsoid given two foci, $(a,b,c)$ and $(d,e,f)$, and one semi-axis $l$? $c$ may not be equal to $f$.
0
votes
2answers
305 views

Find equation of the circular cross section of a unit sphere

I have a unit sphere in Cartesian coordinates: $x^2 + y^2 + z^2 = 1$ or in spherical coordinates: $x = \rho \sin(\phi) \cos(\theta)\\ y = \rho \sin(\phi) \sin(\theta)\\ z = \rho \cos(\phi)$ I ...
1
vote
1answer
54 views

Calculate the center point of multiple lines

I have $n\ge3$ lines $L_i$ given in 3D Space. How do I calculate a point $P$ with minimal $\sum_{i=1}^{n} distance(L_i, P)$?