Spiro

Introduction

Spiro is the creation of Raph Levien. It simplifies the drawing of beautiful curves.

Using bézier splines an artist can easily draw curves with the same slope on either side of an on-curve point. Spiros, on the other hand, are based on clothoid splines which make it easy to maintain constant curvature as well as constant slope. Such curves will simply look nicer.

Raph Levien's spiro splines only use on-curve points and so are easier to use and more intuitive to the artist.

This library will take an array of spiro control points and convert them into a series of bézier splines which can then be used in the myriad of ways the world has come to use béziers.

Programming with libspiro

Types
- spiro control point
- bezier context
Header file
Entry points
- SpiroCPsToBezier(spiros_cp *,int n,int is_closed,bezctx *)
- TaggedSpiroCPsToBezier(spiros_cp *,bezctx *)

Basic Types

The spiro control point

typedef struct {
    double x;
    double y;
    char ty;
} spiro_cp;

    /* Possible values of the "ty" field. */
#define SPIRO_CORNER		'v'
#define SPIRO_G4		'o'
#define SPIRO_G2		'c'
#define SPIRO_LEFT		'['
#define SPIRO_RIGHT		']'

    /* For a closed contour add an extra cp with a ty set to */
#define SPIRO_END		'z'
    /* For an open contour the first cp must have a ty set to*/
#define SPIRO_OPEN_CONTOUR	'{'
    /* For an open contour the last cp must have a ty set to */
#define SPIRO_END_OPEN_CONTOUR	'}'

A spiro control point contains a location and a point type. There are five basic types of spiro control points:

A corner point -- where the slopes and curvatures of the incoming and outgoing splines are unconstrained
A G4 curve point -- Continuous up to the fourth derivative
A G2 curve point -- Continuous up to the second derivative.
A left constraint point -- Used to connect a curved line to a straight one
A right constraint point -- Used to connect a straight line to a curved one.
If you have a contour which is drawn clockwise, and you have a straight segment at the top, then the left point of that straight segment should be a left constraint, and the right point should be a right constraint.

The bézier context

struct _bezctx {
	/* Called by spiro to start a contour */
    void (*moveto)(bezctx *bc, double x, double y, int is_open);

	/* Called by spiro to move from the last point to the next one on a straight line */
    void (*lineto)(bezctx *bc, double x, double y);

	/* Called by spiro to move from the last point to the next along a quadratic bezier spline */
	/* (x1,y1) is the quadratic bezier control point and (x2,y2) will be the new end point */
    void (*quadto)(bezctx *bc, double x1, double y1, double x2, double y2);

	/* Called by spiro to move from the last point to the next along a cubic bezier spline */
	/* (x1,y1) and (x2,y2) are the two off-curve control point and (x3,y3) will be the new end point */
    void (*curveto)(bezctx *bc, double x1, double y1, double x2, double y2,
		    double x3, double y3);

	/* I'm not entirely sure what this does -- I just leave it blank */
    void (*mark_knot)(bezctx *bc, int knot_idx);
};

You must create a super-class of this abstract type that handles the creation of your particular representation of bézier splines. As an example I provide the one used by Raph to generate PostScript output (cubic beziers). Spiro will convert a set of spiro_cps into a set of bezier curves. As it does so it will call the appropriate routine in your bezier context with this information -- this should allow you to create your own internal representation of those curves.

Calling into libspiro

Libspiro needs a header file

#include <spiroentrypoints.h>

You must define a bezier context that is appropriate for your internal splines (See Raph's PostScript example).

You must create an array of spiro control points:

   spiro_cp points[4];

     /* This defines something very like a circle, centered at the origin with radius 100 */
   points[0].x = -100; points[0].y =    0; points[0].ty = SPIRO_G4;
   points[1].x =    0; points[1].y =  100; points[1].ty = SPIRO_G4;
   points[2].x =  100; points[2].y =    0; points[2].ty = SPIRO_G4;
   points[3].x =    0; points[3].y = -100; points[3].ty = SPIRO_G4;

Then call SpiroCPsToBezier, a routine which takes 4 arguments

An array of spiros
The number of elements in the array
Whether this describes a closed (True) or open (False) contour
A bezier context

    bc = new_bezctx_ps();
    SpiroCPsToBezier(points,4,True,bc)
    bezctx_ps_close(bc);

Or call TaggedSpiroCPsToBezier. This routine requires that the array of spiro control points be tagged according to Raph's internal conventions. A closed curve will have an extra control point attached to the end of it with a type of SPIRO_END;

   spiro_cp points[5];

   points[0].x = -100; points[0].y =    0; points[0].ty = SPIRO_G4;
   points[1].x =    0; points[1].y =  100; points[1].ty = SPIRO_G4;
   points[2].x =  100; points[2].y =    0; points[2].ty = SPIRO_G4;
   points[3].x =    0; points[3].y = -100; points[3].ty = SPIRO_G4;
   points[4].x =    0; points[4].y =    0; points[4].ty = SPIRO_END;

(The location of this last point is irrelevant).

An open curve will have the type of the first control point set to SPIRO_OPEN_CONTOUR and the last to SPIRO_END_OPEN_CONTOUR.

   spiro_cp points[4];

   points[0].x = -100; points[0].y =    0; points[0].ty = SPIRO_OPEN_CONTOUR;
   points[1].x =    0; points[1].y =  100; points[1].ty = SPIRO_G4;
   points[2].x =  100; points[2].y =    0; points[2].ty = SPIRO_G4;
   points[3].x =    0; points[3].y = -100; points[3].ty = SPIRO_END_OPEN_CONTOUR;

(In an open contour the point types of the first and last control points are going to be ignored).

In this case there is no need to provide a point count nor an open/closed contour flag. That information can be obtained from the control points themselves. So TaggedSpiroCPsToBezier only takes 2 arguments

An array of spiros
A bezier context

    bc = new_bezctx_ps();
    TaggedSpiroCPsToBezier(points,bc)
    bezctx_ps_close(bc);