Vector Arithmetics in Rhino Python

Today, I am going to advance the Vector class a bit more. Firstly, I will improve the display method I introduced recently. Then, I will add two new methods which handle the fundamental vector arithmetics in Rhino Python.

Improving the Display Method

In the previous attempt, I displayed vectors on the origin of the Rhino viewport. The coordinates of the tail of a vector are not stored within the object attributes. Normally, I can store two coordinates, one for the tail, one for the tip. That seems logical. But in the future, we are going to see that, the actual length of the vector (the amounts of displacement in x, y, and z) will be the core elements of many calculations. This is why I stored only the tip point information. However, while displaying vectors, an origin point can be used. I am adding this optional functionality in the below code:

	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)

The below figure shows the calculation of the vector’s tip point according to the varying origin.

Vector Arithmetics: Vector Addition Method

This method will take two vectors, and output their summation as a new vector. This is one of the fundamental operations we will be using in the future. The below figure explains the vector addition procedure. Thus, it is adding one vector’s tail to the other’s tipping point. Basically, it is the addition of the x, y, and z components of the two vectors.

	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)

Vector Arithmetics: Vector-Scalar Multiplication Method

We will need another important operation: vector-scalar multiplication. When we multiply a vector with a scalar (number), we multiply the components of the vector (coordinates, in our case) by that number. As you can see, the below figure explains this.

	def multiply(self, s):
		v = self.components
		return Vector([v[0]*s, v[1]*s, v[2]*s])

Conclusion: Vector Arithmetics

Today, I started studying vector arithmetics and developed new methods for it. Below is the latest code I have been coding since the beginning.

import rhinoscriptsyntax as rs
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 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])

Now, we can test the above code by creating new vector objects and doing arithmetic operations with them.

myvector1 = Vector([3,5,0])
myvector2 = Vector([4,1,0])
myvector3 = Vector.add(myvector1, myvector2)
myvector1.display([5,5,0])
myvector2.display([5,5,0])
myvector3.display([5,5,0])