Vector Normalization and Dot Product

This is the continuation of the Vector class we started here, and further advanced here, here, and here. This new Rhino Python implementation is mostly educational and partially a hobby. Before this session, we have developed display, magnitude, add, multiply, reverse, and subtract methods. This time, I am adding the vector normalization and dot product methods and seeing the utilizations of the dot product.

import rhinoscriptsyntax as rs
import math
class Vector:
	def __init__(self, point):
		self.components = point
	def display(self, origin=[0,0,0]):
        v = self.components
        tip = (v[0]+origin[0], v[1]+origin[1], v[2]+origin[2])
        line = rs.AddLine(origin, tip)
        rs.CurveArrows(line, 2)
	def magnitude(self):
		v = self.components
		result = v[0]**2 + v[1]**2 + v[2]**2
		return math.sqrt(result)
	def add(vA, vB):
		v1 = vA.components
		v2 = vB.components
		addition = (v1[0]+v2[0], v1[1]+v2[1], v1[2]+v2[2])
		return Vector(addition)
	def multiply(self, s):
		v = self.components
		return Vector([v[0]*s, v[1]*s, v[2]*s])
	def reverse(self):
		return self.multiply(-1)
	def subtract(vA, vB):
		return Vector.add(vA, vB.reverse())
	def normalize(self):
		return self.multiply(1/self.magnitude())
	def dot(vA, vB):
		v1 = vA.components
		v2 = vB.components
		return v1[0]*v2[0] + v1[1]*v2[1] + v1[2]*v2[2]

In the above code, I created a new method for vector normalization, called normalize(). Since we developed a vector-scalar multiplication method earlier, now we can use it to reduce (or increase) the magnitude (length) of any vector to 1 unit. Therefore, the method multiplies the given vector by 1 / its magnitude.

Then, I developed a simple dot product method. The above diagram shows the formula for two-dimensional vectors. Therefore, you can generalize it to n-dimensional vectors by the same formula. Finally, to have a good insight on the dot product I highly recommend watching this and this.