## The Geometry Meaning Of The Determinant

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…

## Rigid Transformation And The Block Matrix

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, Dot Product, Tensor Product In Matrices Forms

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…

## CGAL: Area of Parallelogram And Volume Of Triple Vectors

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.

## Lomo Graphy By OpenCV

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…

## Calculate Distance Between Two Points On A Curve By VTK

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…

## Wolfram – Coordinates and Graphics

Draw a circle and an inner circle Graphics[{Circle[{0, 0}, 1], Circle[{0, -0.5}, 0.5]}] Draw 10 circles which has center (i,i) and i is in {1,10} Graphics[Table[Circle[{i, i}, 0.5], {i, 10}]] Connect 10 points which is at (i,i) data = Table[{i, i}, {i, 10}] ListLinePlot[data] Or: Graphics[Line[data]] ListLinePlot[{{1, 1}, {2, 3}, {3, Read more…

## Remove Vector Weight On Special Axis

We want to calculate a new vector that has no weight on the special axis. Calculate the projected vector on the special axis and remove it, the result is what we want. PointStruct CalculateVectorWeight(PointStruct vec0, PointStruct vec1) { vec0.Unit(); double dotValue = vec1.Dot( vec0 ); PointStruct onVec0 = vec0 * Read more…

3D Model Viewer: add grid plane and convex hull.

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