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## The vector objectThe vector object is not a displayable object but is a powerful aid to 3D computations. Its properties are similar to vectors used in science and engineering. vec(x,y,z) This creates a 3D vector object with the given components x, y, and z. Vectors can be added or subtracted from each other, or multiplied by an ordinary number. For example, var v1 = vec(1,2,3) You can refer to individual components of a vector: v2.x is 10, v2.y is 20, v2.z is 30 It is okay to make a vector from a vector: vec(v2) is still vec(10,20,30). This is a convenient way to make a separate copy of a vector. Currently it is not possible to use
The following functions are available for working with vectors:
mag(A) # calculates length of A It is possible to reset the magnitude or the magnitude squared of a vector: v2.mag = 5 # sets magnitude to 5; You can reset the magnitude to 1 with norm(): norm(A) # A/|A|, normalized; magnitude 1 You can also write v1.norm() or v1.hat. For convenience, norm(vec(0,0,0)) is calculated to be vec(0,0,0). You can change the direction of a vector without changing its magnitude: v2.hat = v1 # changes the direction of v2 To calculate the angle between two vectors (the "difference" of the angles of the two vectors): ang = v1.diff_angle(v2) You can also write v1.diff_angle(v2). For convenience, if either of the vectors has zero magnitude, the difference of the angles is calculated to be zero.
There is a function for rotating a vector: v2 = rotate(v1, angle=a, axis=vec(x,y,z)) The angle must be in radians. The default axis is (0,0,1), for a rotation counterclockwise in the xy plane around the z axis. There is no origin for rotating a vector. You can also write v2 = v1.rotate(angle=theta, axis=vec(1,1,1)). There is also a rotate capability for objects. The JavaScript versions are v2 = rotate(v1, {angle:a, axis=vec(x,y,z}) and v2 = v1.rotate({angle:a, axis=vec(x,y,z}). There are functions for converting between degrees and radians, where there are 2*pi radians in 360 degrees: radians(360) is equivalent to 2*pi |