Geometry - Geo1

Object: Geo1

Geo1 is a special class equipped with a parametric function to describe simple geometries.

The function accepts parametric variable, s (a double) to yield a vector in space (a Vec3). The start and end values of s completes geometric definition.

• s0 : Lower bound of the parametric variable (0 by default)
• s1 : Upper bound of the parametric variable (1 by default)
• f : function in terms of lambda (See c++11 tutorials like Dr. Dobb’s)

Proper way to define lambda is as follows:

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function<Vec3 (double)> f = [=] (double s)->Vec3 {return Vec3(x(s), y(s), z(s));}

Constructors

Geo1() : Creates a geometric definition using default values; (a line between $f(0)$ and $f(1)$);

Geo1(f) : Creates a geometric definition using a new function defined by the default limits

For example, following defines a heart shape;

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Geo1 heart( [](double s)->Vec3 {
     		  	   auto t = 4*atan(1.0)/180*s;
			   return Vec3( (1-sin(t))*cos(t), (1-sin(t))*sin(t));
			   } );

Geo1(s0, s1, f) : Creates a geometric definition using a new function and new limits:

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Geo1 heart(0, 8*atan(1.0), [=](double s)->Vec3 {
     	    	   	return Vec3( (1-sin(t))*cos(t), (1-sin(t))*sin(t));
		    } );

heart.f(1.0) returns a vector with components, $x=1.2$ and $y=3.1$.

Subclasses

Following subclasses consists of the predefined functions (and limits) for simple geometries;

• Geo1Line(x0, x1) defines a line between vectors (Vec3) $x_0$ and $x_1$
• Geo1Circle(x0, r) defines a full circle (in CCW direction) with a center at $x_0$ and a radius of $r$
• Geo1Circle(x0, r, d0, d1) defines an arc from $\theta = d_0$ to $\theta = d_1$ (in degrees) with a center at $x_0$ and a radius of $r$
• Geo1Sine(x0, x1, a, f) defines a sinusodial function between x0 and x1, with an amplitude of a and a frequency of f;