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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">

<head>

<title>vector</title>

<!--

function MM_jumpMenu(targ,selObj,restore){ //v3.0

eval(targ+".location='"+selObj.options[selObj.selectedIndex].value+"'");

if (restore) selObj.selectedIndex=0;

}

//-->

</script>

</head>

<body>

<tr>

If you're new to Python

and VPython: <a href="VisualIntro.html">Introduction</a>

A VPython <a href="VPython_Intro.pdf" target="_blank">tutorial</a>

<a href="primitives.html">Pictures</a> of 3D objects

Choose an object:

<option>Choose an object</option>

<option value="cylinder.html">Overview</option>

<option value="arrow.html">arrow</option>

<option value="convex.html">convex</option>

<option value="curve.html">curve</option>

<option value="cylinder.html">cylinder</option>

<option value="ellipsoid.html">ellipsoid</option>

<option value="extrusion.html">extrusion</option>

<option value="faces.html">faces</option>

<option value="frame.html">frame</option>

<option value="helix.html">helix</option>

<option value="label.html">label</option>

<option value="lights.html">lights</option>

<option value="points.html">points</option>

<option value="pyramid.html">pyramid</option>

<option value="sphere.html">sphere</option>

</select>

Work with objects:

<option>Choose an option</option>

<option value="color.html">Color/Opacity</option>

<option value="materials.html">Materials/Textures</option>

<option value="shapes.html">Shapes Library</option>

<option value="paths.html">Paths Library</option>

<option value="defaults.html">Defaults</option>

<option value="rate.html">Animation Speed</option>

<option value="rotation.html">Rotations</option>

<option value="options.html">Additional Options</option>

<option value="delete.html">Delete an Object</option>

<option value="controls.html">Buttons/Sliders</option>

<option value="graph.html">Graphs</option>

<option value="lights.html">Lighting</option>

<option value="files.html">Read/Write Files</option>

<option value="trail.html">Leaving a Trail</option>

<option value="vector.html">Vector Operations </option>

<option value="factorial.html">factorial/combin</option>

</select>

Windows &amp Events:

<option>Choose a topic</option>

<option value="display.html">Windows</option>

<option value="mouse.html">Mouse Events</option>

<option value="mouse_click.html">   Mouse Click</option>

<option value="mouse_drag.html">   Mouse Drag</option>

<option value="keyboard.html">Keyboard Events</option>

</select>

What's new in <a href="new_features.html">Visual 5</a>

<a href="http://vpython.org" target="_blank">VPython web site</a>

<a href="license.txt" target="_blank">Visual license</a>

<a href="http://www.python.org" target="_blank">Python web site</a>

<a href="http://www.python.org/doc/2.5.2/lib/module-math.html" target="_blank">Math module</a> (sqrt etc.)

<a href="http://www.scipy.org/Documentation" target="_blank">Numpy module</a> (arrays) </td>

<h1 class="Heading-1"> The vector Object</h1>

The 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

high-speed 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

floating-point (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)

v2 = vector(10,20,30)

print(v1+v2) # displays <1 22 33>

print(2*v1)  # displays <2 4 6>

You can refer to individual components of a vector:

v2.x is 10, <span

class="attribute">v2.y is 20, v2.z is 30

It is okay to make a vector from a vector: <span

class="attribute">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 <span

class="attribute">v2.x is the same as v2[0], v2.y is the same as <span

class="attribute">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

mag2(A) = A.mag2 = |A|*|A|, the vector's magnitude squared

norm(A) = A.norm() = A/|A|, a unit vector in the direction of the vector

dot(A,B = A.dot(B) = A dot B, the scalar dot product between two vectors

cross(A,B) = A.cross(B), the vector cross product between two vectors

proj(A,B) = A.proj(B) = dot(A,norm(B))*norm(B), the vector projection of A along B

comp(A,B) = A.comp(B) = dot(A,norm(B)), the scalar projection of A along B

diff_angle(A,B) = A.diff_angle(B), the angle between two vectors, in radians

rotate(A,theta,B) = A.rotate(theta,B) = rotate(vector=A, angle=theta, axis=B), result of rotating A through theta around B

astuple(A) = A.astuple(), convert this vector to a tuple, much faster than using tuple(A)

Some examples:

mag( vector ) # calculates length of vector

mag(vector(1,1,1))  # = sqrt(3) = 1.732...

mag2(vector(1,1,1)) # = 3, the magnitude

squared

You can also obtain the magnitude in the form <span

class="attribute">v2.mag and the square of the magnitude as <span

class="attribute">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

v2.mag2 = 2.7 # sets squared magnitude of v2 to

2.7

You can reset the magnitude to 1 with norm():

norm( vector ) # normalized; magnitude of 1

norm(vector(1,1,1)) = vector(1,1,1)/sqrt(3)

You can also write v1.norm()<span

class="attribute">. 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)<span

class="attribute">. 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 right-hand 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 <a href="rotation.html">rotate capability for

objects</a>.

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 Visual automatically converts (a,b,c) into

vector(a,b,c), with floating-point values, when creating Visual 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().

</td>

</tr>

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</table>

</body>

</html>

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