A review of the dot product and cross product of vectors

Vectors are the basis for 3D graphics processing and image processing; Here we review the basic support:

Quantity product and vector product of vectors:

(1) Number of vectors 1 mass product

(1) vector product of vectors

A cross product (vector product) of two vectors A and B can be defined as:

Here θ represents the angular angle (0°≤θ≤180°) between two vectors, which is located on the plane defined by the two vectors.

< Span style= "font-size:18px" > vector product of modulo (length) can be interpreted as a and b is the adjacent edge of the Span style= "margin:0px; padding:0px; Color:rgb (0,0,0) "> parallelogram area . seek triangle abc area , according to the meaning of the vector product, get:

a=a _{xi +ayj +azk ;}

b=b _{xi +byj +bzk ;}

a xb = (a_{ybz-azby" i+ (azbx-axbz" j + (axby-aybx) k , in order to help the memory, using the third-order determinant, written:}

Calculate the area of a freeform polygon: (vertices are arranged in counter-clockwise order)

To find the most basic method of polygon area is done by the split method, is to divide the polygon into a number of triangles, and then the area for each triangle, the area, in the case of precision requirements, do not use Helen-Qin formula, Helen Formula may be more serious in terms of accuracy loss, and the computational capacity is very large.

The most suitable method to solve the polygon area is the vector product method.

Vertex is P _{k (K=1,2,3...N) polygon with vertex coordinates (x1,y1", (x2,y2), (X3,y3) ... (Xn,yn).}

In computational geometry, we know that the area of ABC is half the absolute value of the two vector cross product "vector ab" and "Vector ac". It indicates whether the triangle vertex is in the right or left-hand line.

A review of the dot product and cross product of vectors