
If you're new to Python A VPython tutorial Pictures of 3D objects What's new in VPython 6 VPython web site 
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. It can be used together with numpy arrays . (numpy is a module added to Python to provide highspeed computational capability through optimized array processing. The numpy module is imported automatically by Visual.) vector(x,y,z) Returns a vector object with the given components, which are made to be floatingpoint (that is, 3 is converted to 3.0). Vectors can be added or subtracted from each other, or multiplied by an ordinary number. For example, v1 = vector(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: vector(v2) is still vector(10,20,30). The form vector(10,12) is shorthand for vector(10,12,0). A vector is a Python sequence, so v2.x is the same as v2[0], v2.y is the same as v2[1], and v2.z is the same as v2[2]. Vector functions The following functions are available for working with vectors: mag(A) = A.mag = A, the magnitude of a vector mag( vector ) # calculates length of vector You can also obtain the magnitude in the form v2.mag and the square of the magnitude as v2.mag2. It is possible to reset the magnitude or the magnitude squared of a vector: v2.mag = 5 # sets magnitude to 5; no change in direction You can reset the magnitude to 1 with norm(): norm( vector ) # normalized; magnitude of 1 You can also write v1.norm(). For convenience, norm(vector(0,0,0)) is calculated to be vector(0,0,0). To calculate the angle between two vectors (the "difference" of the angles of the two vectors). diff_angle(v1,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. cross(A,B) gives the cross product of two vectors, a vector perpendicular to the plane defined by A and B, in a direction defined by the righthand rule: if the fingers of the right hand bend from A toward B, the thumb points in the direction of the cross product. The magnitude of this vector is equal mag(A)*mag(B)*sin(diff_angle(A,B)). dot(A,B) gives the dot product of two vectors, which is an ordinary number equal to mag(A)*mag(B)*cos(diff_angle(A,B)). If the two vectors are normalized, the dot product gives the cosine of the angle between the vectors, which is often useful. You can also say vector1.cross(vector2) or vector1.dot(vector2)). Rotating a vector There is a function for rotating a vector: v2 = rotate(v1, angle=theta, axis=(1,1,1)) The angle must be in radians. The default axis is (0,0,1), for a rotation 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=(1,1,1)). There is also a rotate capability for objects. 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 degrees(2*pi) is equivalent to 360 Convenient conversion For convenience VPython automatically converts (a,b,c) into vector(a,b,c), with floatingpoint values, when creating VPython objects: sphere.pos=(1,2,3) is equivalent to sphere.pos=vector(1.,2.,3.). However, using the form (a,b,c) directly in vector computations will give errors, because (a,b,c) isn't a vector; write vector(a,b,c) instead. You can convert a vector vec1 to a Python tuple (a,b,c) by tuple(vec1) or by the much faster option vec1.astuple(). 
