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<p class="Normal"><a href="vector.html">Vector operations </a></p>
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<h1 class="Heading-1"> <font color="#0000a0">The vector Object</font></h1>
<p class="Normal"> 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
Numeric arrays. (Numeric is a module added to Python to provide
high-speed computational capability through optimized array processing.
The Numeric module is imported automatically by Visual.)</p>
<p class="program">vector(x,y,z)</p>
<p class="Normal"> Returns a vector object with the given components, which are made to be
floating-point (that is, 3 is converted to 3.0).</p>
<p class="Normal"> Vectors can be added or subtracted from each other, or multiplied by an
ordinary number. For example,</p>
<p class="program">v1 = vector(1,2,3)<br />
v2 = vector(10,20,30)<br />
print v1+v2 # displays (11 22 33)<br />
print 2*v1 # displays (2 4 6)</p>
<p class="Normal"> You can refer to individual components of a vector:</p>
<p class="Normal"> <span class="attribute">v2.x</span> is 10, <span
class="attribute">v2.y</span> is 20, <span class="attribute">v2.z</span> is 30</p>
<p class="Normal"> It is okay to make a vector from a vector: <span
class="attribute">vector(v2)</span> is still <span class="attribute">vector(10,20,30)</span>.</p>
<p class="Normal"> The form <span class="attribute">vector(10,12)</span> is shorthand for <span class="attribute">vector(10,12,0)</span>.</p>
<p class="Normal"> A vector is a Python sequence, so <span
class="attribute">v2.x</span> is the same as <span class="attribute">v2[0]</span>, <span class="attribute">v2.y</span> is the same as <span
class="attribute">v2[1]</span>, and <span class="attribute">v2.z</span> is the same as <span class="attribute">v2[2]</span>.</p>
<p class="program"> mag( vector ) # calculates length of vector <br />
mag(vector(1,1,1)) # is equal to sqrt(3)<br />
mag2(vector(1,1,1)) # is equal to 3, the magnitude
squared</p>
<p class="Normal"> You can also obtain the magnitude in the form <span
class="attribute">v2.mag</span> and the square of the magnitude as <span
class="attribute">v2.mag2</span>.</p>
<p class="Normal">It is possible to reset the magnitude or the
magnitude squared of a vector:</p>
<p class="program"> v2.mag = 5 # sets magnitude of v2 to 5 <br />
v2.mag2 = 2.7 # sets squared magnitude of v2 to
2.7</p>
<p class="Normal">You can reset the magnitude to 1 with norm():</p>
<p class="program">norm( vector ) # normalized; magnitude of 1<br />
norm(vector(1,1,1)) equals vector(1,1,1)/sqrt(3)</p>
<p class="Normal">You can also write <span class="attribute">v1.norm()</span><span
class="attribute"></span>. For convenience, <span class="attribute">norm(vector(0,0,0))</span> is calculated to be <span class="attribute">vector(0,0,0)</span>. <span class="attribute"></span> </p>
<p class="Normal">To calculate the angle between two vectors (the "difference"
of the angles of the two vectors).</p>
<p class="program">v1.diff_angle(v2)</p>
<p class="Normal"> You can also write <span class="attribute">v1.diff_angle(v1,v2)</span><span
class="attribute"></span>. For convenience, if either of the vectors has zero
magnitude, the difference of the angles is calculated to be zero<span class="attribute"></span>.</p>
<p class="Normal"> There is a function for the cross product of two vectors,
which is a vector perpendicular to the plane defined by vector1 and vector2,
in a direction defined by the right-hand rule: if the fingers of the right
hand bend from vector1 toward vector 2, the thumb points in the direction
of the cross product. The magnitude of this vector is equal to the product
of the magnitudes of vector1 and vector2, times the sine of the angle between
the two vectors.</p>
<p class="program">cross( vector1, vector2 )</p>
<p class="Normal"> There is a function for the dot product of two vectors,
which is an ordinary number equal to the product of the magnitudes of vector1
and vector2, times the cosine of the angle between the two vectors. If the
two vectors are normalized, the dot product gives the cosine of the angle
between the vectors, which is often useful.</p>
<p class="program">dot( vector1, vector2 )</p>
<p class="Normal">You can also say <span class="attribute">vector1.cross(vector2)</span> or <span class="attribute">vector1.dot(vector2)</span>).</p>
<p class="Normal"><font color="#0000a0">Rotating a vector</font></p>
<p class="Normal"> There is a function for rotating a vector:<font color="#0000a0"></font></p>
<p class="program"> v2 = rotate(v1, angle=theta, axis=(1,1,1))</p>
<p class="Normal">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 <span class="attribute">v2
= v1.rotate(angle=theta, axis=(1,1,1))</span>.
There is also a <a href="rotation.html">rotate capability for
objects</a>.</p>
<p class="Normal">There are functions for converting between degrees
and radians, where there are 2*pi radians in 360 degrees: </p>
<p class="program">radians(360) is equal to 2*pi</p>
<p class="program">degrees(2*pi) is equal to 360</p>
<p class="Normal"><strong><font color="#0000a0">Convenient conversion</font></strong></p>
<p class="Normal"> 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.</p>
<p class="Normal">You can convert a vector <font color="#FF0000">vec1</font> to a Python tuple (a,b,c) by <font color="#FF0000">tuple(vec1)</font> or
by the much faster option <font color="#FF0000">vec1.astuple(</font>).</p>
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