0
votes
1answer
28 views

How can I transform a 3D triangle to xy plane

Suppose I am given a triangle ABC and its corresponding vertex coordinates in 3D. I want to transform ABC in such a way so that vertex A lies on global (0,0,0) coordinate, B lies on (dist, 0, 0) ...
0
votes
1answer
36 views

Triangle in 3D space point X and Y coordinate know find Z

I have a triangle in a 3D space. I know the points X an Y coordinate but I dont know the Z. How can the Z be calculated by knowing the points of the triangle and the X an Y coordinate of the point ...
0
votes
1answer
22 views

Area of triangle on a sphere (not spherical triangle)

How do I find the area of a triangle on a sphere, and the triangle is not a spherical triangle, for example, the triangle is formed with two geodesics and a line of latitude. Is there a specific ...
1
vote
1answer
74 views

Finding the missing coordinate of a point within a 3D triangle

We have an equilateral triangle $ABC$ in 3-dimensional space. The points are known, such as: $A = (x_1,y_1,z_1)$ $B = (x_2,y_2,z_2)$ $C = (x_3,y_3,z_3)$ Point $P$ is on triangle $ABC$. If I know ...
0
votes
0answers
31 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 ...
1
vote
1answer
66 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
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
2answers
236 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 ...
0
votes
1answer
315 views

Determine if projection of 3D point onto plane is within a triangle

In 3D, given three points $P_1$, $P_2$, and $P_3$ spanning a non-degenerate triangle $T$. How to determine if the projection of a point $P$ onto the plane of $T$ lies within $T$?
3
votes
1answer
259 views

Triangle Point Picking in 3D

To take random uniform points inside a triangle Triangle Point Picking method is used. But this is for 2D points, how can I take random points from a triangle that is defined by 3 arbitrary 3D points? ...
0
votes
4answers
160 views

How do you find the area of a triangle in a 3D graph?

How do you find the area of a triangle in a 3 dimensional graph? Is it any different than a regular 2d graph? How would you solve it, if these were your three points? A(1,-4,-2), B(3,-3,-3), ...
0
votes
2answers
488 views

3d geometry: triangle 2 points known, find 3rd point

I have a 3d triangle ABC. Lengths AB, BC, and AC are known. Coordinates of points A and B are known. Point C only the y value of the coordinate is known. I believe there are 2 points that can satisfy ...
0
votes
0answers
132 views

Determining a point in 3D space

So given a point, a rotation around the y-axis, a rotation around the x-axis, and a distance, how can one calculate the relative point in space? For example, the beginning coordinates are (0,0,0). ...
1
vote
3answers
6k views

How to determine if a 3D triangle given by points is a right triangle?

How do I figure out if a triangle is a right triangle in 3-D space if you are given three points: $P = (3, -2, -3)$, $Q = (7, 0, 1)$, $R = (1, 2, 1)$? I know that it is an isosceles triangle (two ...
2
votes
1answer
1k views

How to calculate the rotation matrix between 2 3D triangles?

I need to calculate the rotation matrix and the translation vector between 2 given triangles in Euclidean space. This is really just a rotation and a translation, the lengths of sides of the triangle ...
1
vote
1answer
527 views

3D intersection point between circle and triangle

Given a 3D triangle with vertices $(v0, v1, v2)$ and a 3D circle of radius $r$, centered at $c$, and lying in the plane perpendicular to $axis$, how can I test for intersection points between them? ...
4
votes
3answers
16k views

how to calculate area of 3D triangle?

I have coordinates of 3d triangle and I need to calculate its area. I know how to do it in 2D, but don't know how to calculate area in 3d. I have developed data as follows. ...
0
votes
1answer
150 views

Euclidean Geometry a triangle problem

In the three dimensional figure below, is there a way to prove that $$ \angle MNK = 90^ \circ $$ $\hspace{2.8in}$
0
votes
2answers
1k views

Calculate surface normal of each equilateral triangle in a tetrahedron

How can I calculate the surface normal of each equilateral triangle that makes up a tetrahedron? These are the xyz coordinates of the tetrahedron (+1, +1, +1) (−1, −1, +1) (−1, +1, −1) (+1, −1, −1)
0
votes
2answers
1k views

How do I map a 3D triangle into 2D?

The problem I'm having is mapping a 3D triangle into 2 dimensions. I have three points in x,y,z form, and want to map them onto the plane described by the normal of the triangle, such that I end up ...
0
votes
1answer
126 views

Creating random triangles with points on the radius of a sphere and passing through center

I'm trying to create a pointy "ball" in 3d space using triangles. I want each triangle to pass through a sphere's center, with each point lying on the surface. I can easily make points on the ...
5
votes
3answers
763 views

Largest Triangle with Vertices in the Unit Cube

How would one find a triangle, with vertices in or on the unit cube, such that the length of the smallest side is maximized? And what is that length? A lower bound for the length is $\sqrt{2}$, by ...