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.
4
votes
2answers
387 views
Tranforming 2D outline into 3D plane
I am writing a program where I would like to allow the user to draw 4 connecting lines, such as:
And convert this shape into a 3D plane. Is this possible? Is there an existing algorithm to do so? ...
5
votes
4answers
1k views
Can the Surface Area of a Sphere be found without using Integration?
When we were in school they told us that the Surface Area of a sphere = $4\pi r^2$
Now, when I try to derive it using only high school level mathematics, I am unable to do so. Please help.
5
votes
4answers
5k views
Parametric Equation of a Circle in 3D Space?
So, my dilemma here is... I have an axis. This axis is given to me in the format of the slope of the axis in the x,y and z axes.
I need to come up with a parametric equation of a circle. This circle ...
4
votes
1answer
330 views
Automation of 3D Paper Modeling
I recently saw this creative paper contraption online this prior weekend and wanted to see if I could automate the process of creating all ~35 layers of an equation. Essentially what I would want the ...
1
vote
2answers
66 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 ...
7
votes
3answers
4k 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
2answers
1k views
How to multiply vector 3 with 4by4 matrix, more precisely position * transformation matrix
All geometry in computer graphics are transformed by position * transform matrix; The issue is the fact that position is a vector with 3 components (x,y,z); And transform matrix is a 4 by 4 with one ...
5
votes
1answer
171 views
Uniform distributions on the space of rotations in 3D
I believe on moral grounds that the following three definitions are equivalent, and determine "the" uniform distribution on rotations in three dimensions.
The Haar measure on $SO(3)$.
The uniform ...
4
votes
2answers
1k views
How to transform a set of 3D vectors into a 2D plane, from a view point of another 3D vector?
I googled around a bit, but usually I found overly-technical explanations, or other, more specific Stackoverflow questions on how 3D computer graphics work. I'm sure I can find enough resources for ...
1
vote
3answers
460 views
3D to 2D rotation matrix
I have been trawling through this forum but am struggling to understand the maths a bit. Currently I have a 2D plane within a 3D space and I have the coordinates for them. I want to work on this 2D ...
6
votes
2answers
324 views
How to divide a $3$ D-sphere in “equivalent” parts?
My goal is to put $n$ points on a sphere in $\mathbb{R}^3$ to divide it in $n$ parts, so that their disposition would be as "equivalent" as possible. I don't exactly know what "equivalent" ...
5
votes
1answer
353 views
Find minimum in a constrained three-variable equation
After my last question I have worked through the math quite a bit and now I'm stuck again. This time my question is less wordy.
I have two equations for $t$, one with respect to each $a_{x}$ and ...
4
votes
2answers
281 views
3d transformation two triangles
I have two triangles in 3d. I need to calculate transformation matrix(3X3) between two triangles in 3D.
1)How can I calculate the transformation matrix(rigid) while fixing one of the points to the ...
1
vote
2answers
106 views
Is the value of $\pi$ in 2d the same in 3d? [closed]
I am starting with my question with the note "Assume no math skills". Given that, all down votes are welcomed. (At the expense of better understanding of course!)
Given my first question: What is ...
1
vote
1answer
155 views
How to calculate the direction in which a set of normal vectors (3D) are least oriented?
I have an STL file with thousands of triangular planes with different orientations. What is the best way to calculate the direction in which the normal vectors of the triangles are least aligned?
I ...
1
vote
2answers
247 views
Distance Formula in Three Dimensions
The distance formula in 3-D space is defined as:
$$|P_1\, P_2| = \sqrt{(x_2- x_1)^2 + (y_2 -y_1)^2 + (z_2- z_1)^2}$$
My question is that if I have 2 points that have negative coordinates, do I have ...
1
vote
2answers
70 views
Normal from multiple vectors
I have a several 3D vectors $X_{i}$ which lay approximately in a plane. Now I need to find a single vector, which is normal (as much as possible) to all of them.
For two vectors, I can use a cross ...
1
vote
0answers
194 views
differentiation of polygons, having cross borders
I have point data set and I segmented the data into different planar objects. after that, using contouring (convex hull), I obtained the boundary points. Please assume all points relevant to one ...
1
vote
3answers
405 views
How to show two points in R3 form a plane and determine equation?
Given two arbitrary equidistant points in $R^3$, (p and q), how would one show that they form a plane and what would the equation of that plane be?
Defining two vectors in $R^3: (p - 0)$ and $(q - ...
1
vote
2answers
430 views
3 Rotations to unit vector (3D)
I've been trying to solve this problem for some time now, but I could really need some help:
I have 3 rotations (one per axis) for an object, and want to create a unit vector telling me in which ...
1
vote
1answer
347 views
Find out the border of a planar figure for given a set of points – 2D case
Original post is edited after getting some suggestions;
I am looking for a fast algorithm which is able to detect outer most boundary of a plane for given set of points. Suppose, I have 3D point ...
