Here is a convex object and an origin point outside it. is an arbitrary point in the boundary. Find the farthest point on the boundary along the vector . Name the farthest point . We get a new vector to find the farthest point on the boundary along the direction Read more…
I created a 2D convex hull and wanted to check whether a point is inside it. If the point is inside the polygon, the neighbor cross product vectors have the same directions. If the point is outside, one vector is toward the outside, the other one is toward the inside. Read more…
The geometry meaning of the determinant is the sign volumn value for three vectors in 3D world or a sign area value of two vectors (parallelogram) in the 2D coordinate system. For three points in the 2D world: The triangle is counterclockwise ordered if and clockwise ordered if Read more…
Rotate about z-axis by the angle theta. Verification: So we can get the following conclusions about rotations about x-axis, y-axis and z-axis independently.
The affine transform in the 3D world can be represented by a 4×4 matrix. If there is no scale in the affine transform, the vector is translate vector and A is the rotate matrix. The original point’s position is representing by M, the changed point’s position is M’. Read more…
Cross Product Let’s define vector and and their cross product . As known that , so we have: The cross product is antisymmetric due to its definition. Dot Product So we can write the dot product of two vectors as the matrix form. Read more…
We can get the third vector by cross product of two vectors, the new vector is perpendicular to the first vectors. We also know the geometry meaning of the determinant, it’s sign volumn value for three vectors.
The article shows how to make the original image has a retro style. Two steps need to be done. Change the red color channel of the original image. Change the brightness by a filled circle. The mathematical function used in step1 makes the brighter pixel brighter, darker pixel darker. Read more…
The article shows a way to calculate the length between two points on a curve. We create a ring and put axis actor in the center to show the ring’s orientation and size. Here are implementation details, the data file curve.vtp can be downloaded from my github repository documents. #define Read more…