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<td width="77%"><div align="center"><span class="style1 style2"><font color="#0000A0">curve</font></span></div></td>
<td width="23%"><div align="center"><img src="images/curve.jpg" alt="curve" width="131" height="127" /><a href="arrow.html"></a></div></td>
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<p class="Normal">The curve object displays straight lines between
points, and if the points are sufficiently close together you get the
appearance of a smooth curve. In addition to its basic use for
displaying curves, the curve object has powerful capabilities for other
uses, such as efficient plotting of functions.</p>
<p class="Normal"> Some attributes, such as <span class="attribute">pos</span> and <span class="attribute">color</span>, can be different for each
point in the curve. These attributes are stored as numpy arrays. The
numpy module for Python provides powerful array processing
capabilities; for example, two entire arrays can be added together.
Numpy arrays can be accessed using standard Python rules for
referring to the nth item in a sequence (that is, <span
class="attribute">seq[0]</span> is the first item in <span
class="attribute">seq</span>, <span class="attribute">seq[1]</span> is the second, <span class="attribute">seq[2]</span> is the third,
etc). For example, <span class="attribute">anycurve.pos[0]</span> is
the position of the first point in <span class="attribute">anycurve</span>.</p>
<p class="Normal"> You can give curve an explicit list of coordinates enclosed in
brackets, like all Python sequences. Here is an example of a 2D square:</p>
<div>
<p class="program">square = curve(pos=[(0,0),(0,1),(1,1),(1,0),(0,0)])</p>
<p class="Normal"> Essentially, (1,1) is shorthand for (1,1,0). However, you cannot mix 2D
and 3D points in one list.</p>
<p class="Normal"> Curves can have thickness, specified by the radius of a cross section
of the curve (the curve has a thickness or diameter that is twice this
radius):</p>
<p class="program">curve(pos=[(0,0,0), (1,0,0), (2,1,0)], radius=0.05)</p>
<p class="Normal"> The default radius is 0, which draws a thin curve. A nonzero radius
makes a "thick" curve, but a very small radius may make a curve that is
too thin to see.</p>
<p class="Normal"> In the following example, the <span
class="attribute">arange()</span> function (provided by the Python
numpy module, which is imported by the Visual module, gives a
sequence of values from 0 to 20 in steps of 0.1 (not including the last
value, 20).</p>
<p class="program">c = curve( x = arange(0,20,0.1) ) # Draw a helix<br />
c.y = sin( 2.0*c.x )<br />
c.z = cos( 2.0*c.x )</p>
<p class="Normal"> The <span class="attribute">x</span>, <span
class="attribute">y</span>, and <span class="attribute">z</span> attributes allow curves to be used to graph functions easily:</p>
<p class="program">curve( x=arange(100), y=arange(100)**0.5, <br />
color=color.red)</p>
<p class="Normal"> A function grapher looks like this (a complete program!), where "raw_input" is a Python function that accepts input typed in the Python Shell window:</p>
<p class="program"> eqn = raw_input('Equation in x: ')<br />
x = arange( 0, 10, 0.1 )<br />
curve( x=x, y=eval(eqn) )</p>
<p class="Normal">Parametric graphing is also easy:</p>
<p class="program">t = arange(0, 10, 0.1)<br />
curve( x = sin(t), y = 1.0/(1+t), z = t**0.5,<br />
red = cos(t), green = 0, blue = 0.5*(1-cos(t)) )</p>
<p class="Normal"> Here are the curve attributes:</p>
<p class="attributes"> <span class="attribute">pos[]</span> Array of
position of points in the curve: pos[0], pos[1], pos[2]....<br />
The current number of points is given by len(curve.pos)</p>
<p class="attributes"> <span class="attribute">x[ ]</span>, <span
class="attribute">y[ ]</span>, <span class="attribute">z[ ]</span> Components of pos; each defaults to [0,0,0,0,...]</p>
<p class="attributes"> <span class="attribute">color[ ]</span> Color
of points in the curve</p>
<p class="attributes"> <span class="attribute">red[ ]</span>, <span
class="attribute">green[ ]</span>, <span class="attribute">blue[ ]</span> Color components of points in the curve</p>
<p class="attributes"> <span class="attribute">radius</span> Radius of
cross-section of curve<br />
The default radius=0 makes a thin curve</p>
<p class="attributes"><span class="attribute">material</span> Material
for a thick curve; see <a href="materials.html">Materials</a> for
currently available options</p>
<p class="Normal">Currently it is not possible to specify the opacity
of a curve object.</p>
<p class="Normal"><strong><font color="#0000a0">Adding more points to a curve</font></strong></p>
<p class="Normal"> Curves can be created incrementally with the <span
class="attribute">append()</span> function. A new point by default
shares the characteristics of the last point.</p>
<p class="program">spiral = curve( color = color.cyan )<br />
for t in arange(0, 2*pi, 0.1):<br />
spiral.append( pos=(t,sin(t),cos(t)) )</p>
<p class="Normal"> One of the many uses of curves is to leave a trail
behind a moving object. For example, if <span class="attribute">ball</span> is a moving sphere, this will add a point to its trail: </p>
<p class="program">trail = curve()<br />
ball = sphere()<br />
# .... Every time you update the position of the ball:<br />
trail.append(pos=ball.pos)</p>
<p class="Normal">When appending to a curve, you can optionally choose to retain only the last N points, including the one you're adding:</p>
<p class="program">trail.append(pos=ball.pos, retain=50) # last 50 points</p>
<p class="Normal"><strong><font color="#0000a0">Interpolation</font></strong></p>
<p class="Normal"> The curve machinery interpolates from one point to the next. For
example, suppose the first three points are red but the fourth point is
blue, as in the following example. The lines connecting the first three
points are all red, but the line going from the third point (red) to
the fourth point (blue) is displayed with a blend going from red to
blue.</p>
<p class="program">c = curve( pos=[(0,0,0), (1,0,0)], color=color.red)<br />
c.append( pos=(1,1,0) ) # add a red point<br />
c.append( pos=(0,1,0), color=color.blue) # add blue point</p>
<p class="Normal"> If you want an abrupt change in color or thickness, add another
point at the same location. In the following example, adding a blue
point at the same location as the third (red) point makes the final
line be purely blue.</p>
</div>
<div>
<p class="program">c = curve( pos=[(0,0,0), (1,0,0)], color=color.red)<br />
c.append( pos=(1,1,0) ) # add a red point<br />
c.append( pos=(1,1,0), color=color.blue) # same point<br />
c.append( pos=(0,1,0) ) # add blue point</p>
<p class="Normal">Technical note: No matter how many points are in
a curve, only 1000 are displayed, selected evenly over the full set
of points, in order that the display of a very long curve doesn't slow
down unacceptably. </p>
<p class="Normal">See description of <a href="options.html">Additional
Attributes</a> available for all 3D display objects.</p>
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