-1
votes
1answer
37 views

How to rotate a line in 3d space?

I am trying to figure out direction vectors of the arrowheads of an arrow. Basically I'm given a normalized direction vector ...
0
votes
2answers
22 views

How to find a normal vector from an equation in the form f(x,y)?

If I have an equation $f(x,y)$ which given the $x$ and $y$ coordinate, it gives you the $z$ coordinate. How can I find the normal (directional) vector of the the point $(x,y,f(x,y))$? This would be ...
1
vote
0answers
8 views

Why is tree traversal the fastest ray-box method?

I'm learning ray tracing (the problem of intersecting a ray, aka a vector, against a 3D box defined by a max and a min point) and I'm wondering: why is a tree traversal (e.g. bounding volume ...
0
votes
1answer
20 views

How to rotate a 3d vector to be parallel to another 3d vector using quaternions?

I have a vector (a,b,c) and another vector (d,e,f). I'm trying to rotate (a,b,c) so its parallel to (d,e,f) using quaternions. I need help understanding how I would do this. I have so far that a ...
0
votes
0answers
23 views

Shooting a grenade - angle throwing

In my 3D simulation/game I need to shoot a grenade from a grenade launcher. The movement of the grenade is already setup by someone else. all I need is to give him the pitch angle of the grenade ...
0
votes
3answers
41 views

Determining if a point is inside two planes

I have two planes(Plane 1 and Plane 2) the normals ($n_1$ and $n_2$) of which are known to me. How do I determine if a point is inside the two planes? By inside I mean the 3d space between Planes 1 ...
0
votes
1answer
24 views

Linear Algebra: finding specific linear combinations which meet the criteria

Consider any three vectors u,v,w in 3-dimensional space s.t joining the three vectors by straight lines forms a triangle. Under what condition on c,d,e will the combination cu + dv + ew fill the ...
0
votes
1answer
47 views

Find tangent vector to surface given a point on the surface and its normal vector (for a sphere)

I need to know how to find a tangent vector to a point on the surface of a sphere if I am given the point P and the normal vector at that point N. I know that there are many possible tangent vectors ...
1
vote
2answers
40 views

Problem with vector multiplication

I have this plane problem and the answers are released for it. I don't understand this specific part: Why does : (i + 4k) x (3j - k) = -12i + j + 3k. I tried using the cross product method, however, ...
3
votes
2answers
77 views

What is (fundamentally) a coordinate system ?

Consider the following construction of vectors and points. Let's start with a vector space, or more specifically a coordinate space $F^N$ over a field $F$ and of $N$ dimensions. The elements of this ...
0
votes
1answer
56 views

How to calculate the points of the triangles making up an Octahedron?

Ok guys, I'm not a great mathematician but will try to work this as accurately as I can. I hope someone can help me. I am drawing some 3D objects and I am having trouble drawing an Octahedron. I ...
0
votes
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 ...
1
vote
1answer
421 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 ...
5
votes
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 ...
1
vote
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 ...
2
votes
2answers
107 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
0answers
20 views

Resolving bearings for tilted structure (vector rotations)

I am trying to find a neat solution to resolving bearings for a tilted structure. For example, if I know that a hub is $268.74^{\circ}$ and offset ($X = -3.542 $m, $Y = -1.857$ m, $Z = 2.013$m) with ...
0
votes
0answers
39 views

Finding the Y position of a point between four points on a plane in 3d space

I have been wracking my mind for a while about this... I recently created a function which would utilise Perlin noise to create a 3D pseudo-randomised landscape (and return it as a two-dimensional ...
1
vote
0answers
28 views

sweeping edges till they get a given elevation on an oblique plane

I am constructing wireframe model of 3d objects (prisms,..etc.). from a triangular mesh, I have obtained boundary points and fit striaght lines in order to get polygon edges refering to prism ...
0
votes
0answers
59 views

Are these two sets of rotations about an arbitrary axis and then about the y-z axes equivalent?

Suppose I have a situation where I have to turn an object about an arbitrary axis located on the y-z plane by an angle theta so that it finally reahes orientation 2. Now, can I reach orientation 2 ...
1
vote
0answers
70 views

Mathematical Basis for Dimetric Projection

For a school project, I need to make a program that can plot $y = f(x,z)$ using a form of dimetric projection. I was given the projection formulae $$\begin{align*} x' &= x + sz\cos(\theta)\\ y' ...
2
votes
1answer
366 views

Angle between different rays (3d line segments) and computing their angular relationships

I have several positions (say A,B,C,..) and I know their coordinates (3d). From each point, if a certain ray is passing in a way to converge them at a given (known) point (say O). This point O ...
0
votes
2answers
458 views

Calculate distance from plane to parallel plane in O using vector and normal

I'm trying to figure out what's the best method to get the distance between two planes where i have the normalized vector of the plane and a point in the plane. What I want to do is to create a ...
3
votes
1answer
238 views

Finding intersection of 2 planes without cartesian equations?

The planes $\pi_1$ and $\pi_2$ have vector equations: $$\pi_1: r=\lambda_1(i+j-k)+\mu_1(2i-j+k)$$ $$\pi_2: r=\lambda_2(i+2j+k)+\mu_2(3i+j-k)$$ $i.$ The line $l$ passes through the point with ...
2
votes
4answers
126 views

Why can a plane be defined with its normal line?

The title is worded a bit confusingly. I apologize, I just couldn't think of how to phrase it. Either way, say you have the plane $x+2y-4z=8$ The normal line will have direction $x=1, y=2, z=-4$ So ...
0
votes
0answers
68 views

Turn any shape to circle

I'm looking at trying to calculate and re position 3d vectors to align in a new position to form a circle. I've achieved this already however only when all points are evenly distributed in the same ...
1
vote
2answers
109 views

Calculating new vector positions

I'm using the following formula to calculate the new vector positions for each point selected, I loop through each point selected and get the $(X_i,Y_i,Z_i)$ values, I also get the center values of ...
1
vote
1answer
176 views

Calculate vector position

I'm trying to calculate & move vertices to their average "radius" and form a circle from these new positions. Example: I have 8 vertices selected, I have a little script in Maya that will iterate ...
0
votes
1answer
43 views

New vector position

How can I calculate the new position of a 'point', with just a distance value coming from the center of the selection. Example: I have 8 vertices selected, I have a little script in Maya that will ...
1
vote
1answer
95 views

How can I find the position vector?

There are two planes intersecting at a line. Plane 1: $x - 2y + z - 9 = 0 $ Plane 2: $x + y - z + 2 = 0$ There is a point $A = (p, q, 1)$ on the line of intersection. How can I find $p ...
1
vote
1answer
300 views

How to generate an ordered list of vertices of a cube from a face and a normal vector

Consider a cube with faces we'll call "left", "right", "front", "back", "top" and "bottom". The cube can be described by $0 \le x,y,z \le 1$. To name the faces, we'll say $x$ extends to the right, ...
1
vote
1answer
2k views

How to find perpendicular distance from point to plane in 3D

The line $L_1$ passes through point $A$ whose position vector is $3i - 5j + 4k$, and is parallel to the vector $3i + 4j + 2k$. The line $L_2$ passes through the point $B$ whose position vector is $2i ...
2
votes
1answer
40 views

least number of planes intersecting a finite number of points in space, but not intersecting origin.

Let $$\mathbb{R}^*=\mathbb{R}-\{0\}$$ and $$N=\{0,...,n\}$$ and $$\mathcal{M}=\{ A\subseteq \mathbb{R}^3\times\mathbb{R}^* \mid (\forall\mathbb{x}\in N^3:\mathbb{x}\ne 0)(\exists(\mathbb{a},d)\in ...
0
votes
1answer
110 views

How to move a one 3D line from three 3d parallel lines

I have 3 parallel line segments (say AB, CD, and EF are line segments and they are nearly horizontal) lay on 2 slanted planes which have been intersected through the CD. If I projected all the line ...
2
votes
2answers
2k views

Point on the left or right side of a plane in 3D space

I have an alpha plane determined by 3 points in space. How can I check if another point in space is on the left side of the plane or on the right side of it? I need a fast solution for plug-in ...
0
votes
2answers
439 views

3D Cartesian Coordinates System revolve around a specified axis

I have a 3d cartesian coordinates system and now I want to rotate a point $p(x_0, y_0, z_0)$ arround a specified axis $v(v_x, v_y, v_z)$ like $(1,1,1)$,and the angle is $\theta$,finally I want to get ...
0
votes
1answer
71 views

particle with radius 'r' hits the plane. what is the point of contact?

A large particle with radius r hits the plane with perpendicular 'n' and passing through ,q'. I need to check whether it hits the plane or not. In order to do that I need to find the point of contact. ...
1
vote
1answer
168 views

Given velocity and position, when does it hit the plane?

A particle at position $p$ and velocity $\vec{v}=\langle x,y,z \rangle$ hits the plane orthogonal to vector $\vec{n}$ and passing through point $q$. When does the particle hit the plane? I calculated ...
2
votes
1answer
202 views

How to recover three successive rotations of a vector

I have a vector, which I rotated with respect to $x$, $y$ and $z$ axes, respectively. Now I want to recover this operation, that means I want to bring it to the previous position by rotating it with ...
11
votes
6answers
15k views

Calculate Rotation Matrix to align Vector A to Vector B in 3d?

I have one triangle in 3d space that I am tracking in a simulation. Between time steps I have the the previous normal of the triangle and the current normal of the triangle along with both the current ...
2
votes
1answer
233 views

Calculating angle of human joint beyond 180° in 3D

I'm having some trouble calculating the angle of an human joint in 3D using the Microsoft Kinect. Here's an example of the angle of the elbow (using the shoulder and wrist joint): Image of example ...
0
votes
0answers
84 views

Can 2 parallel lines be discriminated as 'away', 'beside' with respect to 3rd parallel line?

I have nearly parallel several 3D line segments. some line segments locate (blue line) beside to a spefic line segment (black line) and some other (red line) locate away from that line segment. i want ...
3
votes
2answers
659 views

Extend angle between two 3D vectors to x-y plane.

I would like to know how I can extend the angle between two vectors in 3D space to the x-y plane. So, there are two vectors in 3D space, and the angle between them is found using the definition of ...
0
votes
1answer
534 views

line projection on top of a plane

If I have a horizontal line (a 3d point and 3d vector with zero z component) and another plane (could be an oblique or a horizontal; i have normal vector of the plane); then how do we get the ...
3
votes
0answers
638 views

Three-dimensional vectors and force systems

Full disclosure: this is a homework problem. However, I find myself stuck in the middle. The problem is below As shown, a system of cables suspends a crate weighing W = 350 . (Part C 1 figure) ...
0
votes
0answers
305 views

3D Mathematics Projecting One Vector onto Another

I have a Vector function which takes two Vectors and and attempts to "project" these vectors together. The method used is to separate the larger of the two vectors (the larger value calculated via ...
2
votes
1answer
228 views

Projecting a 3D vector to a screen, with the size $X\times Y$?

I am currently programming something, and I'm stuck on how to take a 3D vector, then project it on a screen. Say $X_s$ = the screen width and $Y_s$ = the screen height, Pa = pitch and $Y_a$ = yaw, ...