Vectors have length, direction and angle. In engineering and science, vectors can be moved tip to tail to add forces and create a resultant vector. Vectors are equal if magnitude and direction are equal. Position is arbitrary. 2D vectors can fully describe with one (x,y) pair. When the vector starts at (0,0), the end point is also the delta x and delta y.
The autocad line already has everything it needs to be a vector. The direction is saved in separate variables for start and end point. The acadline object in VBA has all the properties required of a vector – StartPoint, EndPoint, Length, Angle and Delta. Delta is the vector. Delta is returned as a 3 place array of doubles, exactly the same as StartPoint and EndPoint, but it’s not a point, it’s (x2-x1, y2-y1, z2-z1). We save it to a variable as if it were a point. We use it to do vector algebra – the algebra of lines.
An object vector is given a variable name, such as U, V, W, S or T, usually lower case and bold, and specified to be equal to the delta values.
angle brackets (this wordpress is html and it will not allow angle brackets for any purpose other than the one it has in its mind) are used to show (x,y) (imagine angle brackets) is not the same thing as (x,y).
Vectors are added by adding their delta values. if u = (ux,uy) and t = (tx,ty) then u + t = (ux+tx, uy+ty). Vectors can also be subtracted and scaled. The angle and length they make can be calculated from the delta. Vectors of different length and angle are easily added to form a new vector with new length and new direction.
A great deal of engineering mechanics and physics vector work can be done just by drawing lines of appropriate length and direction and moving the vectors tip to tail, measuring the resultants.
The parallelogram rule states that if two vectors are to be added, draw them as adjacent sides of a parellogram, the diagonal is the sum. If 3 or more vectors to be added, they are moved one after the other and the resultant is start point to finish.
The math of adding, subtracting and scaling vectors is simple. Creating a vector class in VBA allows the formation, properties and rules of calculations to be formalized. This is a first simple draft.
Vectors in different locations with the same length and direction are declared equal. Math is done on vectors regardless of position. If a vector start point is at 0,0, that is declared to be standard position. In order to physically draw the vector in autocad, we have to have a position. So we may want to specify vectors assuming the start point is 0,0 with length and angle parameters. Or we may want to specify with a single point value as the endpoint. Other vectors we may want to specify the start point and parameters. That gives us 5 possible ways to specify a vector. The first two assume 0,0 as the start point. Using (x1,y1) as start point, and (x2,y2) as endpoint –
vector2 (Length, Theta)
vector3 (x1,y1, x2,y2)
vector4 (x1,y1, Length, Theta)
vector5 (x1,y1,x_delta, y_delta)
In VBA classes, the variables used may be hidden from the user, while the names of property subs are the interface. We use the good names for properties and reference names for the variables. We want (i think) to save all required data even though it is redundant. The angle and length can be calculated from the point values, and vice versa, so they have to be consistent.
property names – variables
3 place array of doubles
pt1 – startpt1
pt2 – endpt2
delta – pdelta
angle – pangle
length – plength
delta_x – pdelta_x
delta_y – pdelta_y
x1 – px1
x2 – px2
y1 – py1
y2 – py2
Properties are implemented with Get (return of value from variable) and Let (assignment of value to variable) statements. The easiest way to start them is to use the VBA editor pulldown under Insert Procedure and click Property. It will add each. We dont really need Let statements yet in this first implementation. Variables are assigned when the vector is first initialized in a single sub procedure. (I am going to post screenshots while this is still in a state of flux.)
The angle of the vector can be calculated from Tangent of delta y over delta x, but tangent has a period of 180 degrees and vectors rotate from 0 to 360, not including 360, so i wrote a simple program to test in each quadrant.
When the vector is specified with length and angle, the initialization sub can be shortened, so it is not redundant. (SLA here stands for Start, Length, Angle)
The vector.draw method –
This arrow is not integral. It is a 1-unit long block inserted at the end point of the line at a scale that looks good using the angle of the vector. The vector line is full length of course, so on-screen calculations work. The arrow can be erased. A switch could be added in a more polished program to arrow or not arrow. The optional parameter adds a text label at the midpoint of the vector.
This is all we need to get started with vectors. The calculation programs are external to the class.
Here is a test demo and the autocad output.
The math is simple, but we will not be able to use VBA symbols “+ – *” for vector addition, subtraction and multiplication. Those are reserved. Subtraction is accomplished by using a -1 scalar factor and adding the negative vector. Functions return a vector object. We need to set up a vector variable to receive the result.
another interesting application of the parallelogram rule is that one diagonal is the sum, the other is the difference.