2
votes
1answer
26 views

Collinear points in 3dimension

Given three $3D$ points: $A,B$ and $C$, what is the procedure to check if they are collinear? In general, given $n$ points in $m$-dimension, how should one find out, if these $n$-points defines a ...
0
votes
2answers
33 views

Unusual 3D Packing Problem

I made up this interesting problem playing with wire sculptures: If I have a $10 \times 10 \times 10$ clear box and inside I can put wireframe unit cubes, what's the maximum number of unit edges (or ...
0
votes
0answers
15 views

Solving for and x,y,z coordinate in a 3D plane

This is hard for me to explain, but basically I am making a game and I want a 3rd person like camera. I have a lot of information about how the camera should be but I can't seem to get the camera to ...
0
votes
0answers
17 views

Find the normal of a polygon with vertices that are not linearly independent in 3d

For example, take the vectors: $(1,2,3) (4,5,6) (7,8,9) (10,11,12) (13,14,15)$ What would the normal to the polygon be? I'm guessing it would be $(0,0,0)$? For vertices that are linearly ...
1
vote
2answers
33 views

Is the rhombic dodecahedron the only isohedral polyhedron that tiles 3-space (other than the cube)?

Is the rhombic dodecahedron the only face-transitive (or isohedral, i.e. all faces are the same) polyhedron that seamlessly tiles 3-dimensional Euclidean space (other than the cube)? I'm looking ...
0
votes
0answers
9 views

Creating a Cube-based 3-Dimensional Game [migrated]

I am trying to create a 3-dimensional game that is based entirely off of cubes of the exact same size. I wanted to learn how to make my own 3-dimensional game using only 2-dimensional game libraries. ...
0
votes
1answer
27 views

Finding the counter-clockwise direction of points in 3d

I have a set of 5 points of a polygon in 3d. I want to order these points in a counter-clockwise direction. How do I do this? In 2d, to check if two points are ordered counter-clockwise or ...
1
vote
1answer
34 views

Incenter of Triangle in 3D

I'm trying to figure out how to find the incenter of a triangle with (x, y, z) coordinates for the verteces. I can find the lengths of the sides and the radius of the incircle from that, so I've ...
0
votes
1answer
25 views

Find vector rotated on 3D plane

I don't have access to a computer so I can't give pictures but I will try to make this easy to visualize. Suppose I have a vector $n$. I will now draw a plane normal to this vector that and have that ...
0
votes
1answer
27 views

clockwise or counter clockwise in 3D

I have two different situation that I need to make distinction between them (shown in the picture). In other words, in (A) points 3 and 4 are in right and left side of line 1-2. However, in case (B) ...
0
votes
0answers
28 views

Distance from a point to the walls of a cube in 3D

I have defined six different planes that constitute a cube($6$ plane equations). I place an object within the cube at a point $P_1 \equiv (X_c,Y_c,Z_c)$. There are $6$ cameras on the object pointing ...
0
votes
0answers
21 views

Partition of the 3d space with circles?

Does it exist a partition of the 3d space with circles of positive radium? I know the answer is no for a plane, but I can not transpose my demonstration to the space and I have no clue on how to do ...
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
17 views

This is regarding 3d parametarization and vectors.

Generally, I have a hard time conceptualizing how to sketch a vector that looks like $(\cos t, \sin t, t)$. How do I approach this? Usually, in an examination, there are really small bounds given so ...
1
vote
1answer
50 views

How to find out if four points are on the same plane, only by using distances?

There is a method called Cayley-Menger determinant in order to find if 3 points are collinear, 4 points are coplanar etc. provided that all the pairwise distances are given. However, in 2-D, there is ...
0
votes
0answers
12 views

What is the offset curve of a 2D slice of the 3D offset of a twisted swept figure

I have a simple 2D shape as below helically swept. I then do an offset in 3D from the surface. to get if I take a 2D cross section I then get As you can see the offset curve of the 2D ...
0
votes
0answers
26 views

How to define a binormal equation using 3D coordinates, with given sine wave function?

I am attempting to implement in code the math and functions found here: http://http.developer.nvidia.com/GPUGems/gpugems_ch01.html So this question is contextual to that article, I'm sorry for that, ...
0
votes
2answers
29 views

Scale a Point onto Plane

I'm trying to find the scale factor that scale a point onto plane in 3D Space. I have the following information: Point on a plane: $a = (x_1,y_1,z_1)$ Plane equation: $P\colon Ax + By + Cz +D =0$; ...
1
vote
1answer
29 views

How to Create a Plane Inside A Cube

I have a $e \times e \times e$ cube and I want to create random planes with equation $ax + by + cz + d = 0$ inside this cube. I will put random points on those randomly created planes as well. Here ...
1
vote
1answer
22 views

Find $z$ of a point in a plane in 3D space

Say for example, I have 4 points which I know the coordinates to, how can I find a fifth point that lies somewhere within them? E.g, if $A(0,0,a)$, $B(1,0,b)$, $C(1,1,c)$ and $D(0,1,d)$ lie in a ...
1
vote
2answers
45 views

How to Represent a 3D Line under Polar Coordinates

In one of my applications, I need to represent a line under 3D polar coordinates system. In 2D, we can define a line by a distance to the origin and then a angle indicating the direction of the line ...
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 ...
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 ...
1
vote
0answers
35 views

How many edges is sufficient to check to prove polyhedron convexity?

Consider the set $\{u_{1}, u_{2}, \ldots, u_{n}\}$ of points on the spere in $\mathbb{R}^{3}$ (i. e. $||u_{i}|| = 1$) and their convex hull C = $Hull(u_{1}, \ldots, u_{n})$. It's obvious that each ...
-1
votes
1answer
49 views

Rotate the Points on a Plane $P = ax+by+cz + d = 0$ parallel to $z = 0$ plane

I have a plane $P = ax+by+cz + d = 0$ and many points on that plane. I want to rotate $P$ so that it becomes parallel to $z = 0$ plane. Which method should I use? I know that the normal vector of my ...
0
votes
1answer
65 views

Rotation formalisms in three dimensions

I'm little bit confused. The Rotations are described by various means Direction Cosines Matrix (DCM); Euler Angles; Euler Axis/Angle; Quaternion. What is the difference between them. How I can ...
2
votes
1answer
77 views

How To Generate Random Points on the Positive Side of a Plane in 3-D

Edit: The question can also be interpreted as: How to generate random coplanar points in a cube? Here is what I am struggling with: I have a cube, whose origin is $(0,0,0)$ and one edge length ...
3
votes
1answer
55 views

Check if a point is on a plane? (Minimize the use of multiplications and divisions)

In $\mathbb R3$, given a plane $\mathcal P$ defined by three 3D points points $v_0, v_1, v_2$, I want to check if another point $p$ belongs to that plane, while avoiding the use of multiplications and ...
0
votes
1answer
34 views

How to generate a 3D spherical symmetric object from a 2D circular graph

I have a very simple 2d graph. 6 lines separated by equal angle of 60 degrees radiate from the center of a 2d circle, intersecting with the circumference at 6 points. Suppose I know the coordinates ...
0
votes
2answers
87 views

Finding the missing vertex $(x,y,z)$ of a rectangle whose other vertices are defined.

How do I find the missing fourth vertex $D$ of a rectangle, which has three vertices defined? The Equation of the plane being $ax+by+cz+d=0$ Where, $a = (By-Ay)(Cz-Az)-(Cy-Ay)(Bz-Az)$ $b = ...
0
votes
0answers
27 views

Surface comparison using the vertex information and normal vectors

I have two point clouds with normal vector information. How can I use the normal vector information to measure the surface similarity of these two point clouds?
1
vote
0answers
24 views

What should happen to an impossible cube at a vertex?

I have automated the process of impossible-cube renders in Blender3D as an exercise. However, while the automator works fine as long as the intersection of the 'impossible' edge and the nearer edge is ...
0
votes
1answer
47 views

4 floats to determine a plane?

I am taking up a programming and asked to create a function for a certain problem. I was given this struct for a plane. However I can't make sense of this struct. How can 4 floats determine a plane in ...
0
votes
1answer
96 views

Given 4 corner points of a rectangle in 3d space, how to find its “plane” equation?

Context: A BoundingPolytope defines a polyhedral bounding region using the intersection of four or more half spaces. The region defined by a BoundingPolytope is always convex and must be closed. ...
0
votes
1answer
72 views

Basic 3D geometry problem

Here's 1 lb of butter What is the area of the wrapper around it? My answer : 4(11,5 * 6,3) = 289,80cm^2 2(6,3 * 6,3) = 79,38cm^2 289,80 + 79,38 = 369,18cm^2 A = 369,18cm^2 Teacher's answer : A ...
0
votes
0answers
53 views

Estimating the geometric shape of a point cloud without using the vertex information

Consider a point cloud format that describes 3D point clouds by vertices, triangle labels and normal vectors. If we miss the vertex information, is it possible to retrieve the lost data by triangle ...
0
votes
1answer
63 views

Ellipse Tangents in 3D

I know that we can find the tangent of the ellipse in 2D by taking the derivative of the equation defining the ellipse. But I'm little bit confused about finding the ellipse tangent in 3D. Where the ...
1
vote
1answer
39 views

Find intersection of 2 parameterized planes

I have two parameterized planes, for example, {u, 0, v} and {u-1, v-1, 1}. And I have to find the parametric equation of the line that intersects both planes. By setting both planes equal to each ...
0
votes
0answers
18 views

How to find the values of transformstion and its center/axis? [duplicate]

I have system of two planes. Each plane is defined by three points, so I have their equations. One of these plane is stable, I can't perform any transformation. The second one is modifiable - rotation ...
0
votes
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 ...
0
votes
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 ...
0
votes
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 ...
1
vote
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 ...
0
votes
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 ...
2
votes
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?
-1
votes
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 ...
2
votes
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 ...
5
votes
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? ...
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 ...
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 ...