Add quadractic and cubic Bezier curves to custom symbols language

doc/rst/source/changes.rst

@@ -6,6 +6,15 @@
 Changelog
 =========
 
+New Features in GMT 6.7
+=======================
+
+* Add quadratic (**Q**) and cubic (**B**) Bezier curve commands to the custom symbol
+  macro language, enabling smooth curves in ``.def`` symbol files.  Both commands
+  extend the path from the previous **M** or **D** point; **Q** takes one control point
+  plus endpoint, **B** takes two control points plus endpoint.  See
+  :ref:`Custom Symbols <custom-symbols>` for details.
+
 New Features in GMT 6.6
 =======================
 

doc/rst/source/reference/custom-symbols.rst

@@ -145,6 +145,8 @@ are constants.
 +===============+============+========================================+============================================+
 | arc           | **A**      | Append circular arc to existing path   | :math:`x_c, y_c, d, \alpha_1, \alpha_2`    |
 +---------------+------------+----------------------------------------+--------------------------------------------+
+| cubicbezier   | **B**      | Cubic Bezier from last point           | :math:`cx_1, cy_1, cx_2, cy_2, ex, ey`     |
++---------------+------------+----------------------------------------+--------------------------------------------+
 | drawto        | **D**      | Draw line from previous point          | :math:`x, y`                               |
 +---------------+------------+----------------------------------------+--------------------------------------------+
 | moveto        | **M**      | Set a new anchor point                 | :math:`x_0, y_0`                           |
@@ -179,6 +181,8 @@ are constants.
 +---------------+------------+----------------------------------------+--------------------------------------------+
 | pentagon      | **n**      | Plot a pentagon                        | :math:`x, y, size`                         |
 +---------------+------------+----------------------------------------+--------------------------------------------+
+| quadbezier    | **Q**      | Quadratic Bezier from last point       | :math:`cx, cy, ex, ey`                     |
++---------------+------------+----------------------------------------+--------------------------------------------+
 | rect          | **r**      | Plot a rectangle                       | :math:`x, y, width, height`                |
 +---------------+------------+----------------------------------------+--------------------------------------------+
 | roundrect     | **R**      | Plot a rounded rectangle               | :math:`x, y, width, height, radius`        |
@@ -200,6 +204,16 @@ are constants.
 | plus          | **+**      | Plot a plus sign                       | :math:`x, y, size`                         |
 +---------------+------------+----------------------------------------+--------------------------------------------+
 
+Note for **B** and **Q**\: Both Bezier commands extend the current path from the
+*last point set by* **M** *or* **D** (the implicit start point :math:`P_0`); you do not
+supply :math:`P_0` explicitly. **B** takes two control points followed by the endpoint
+(:math:`cx_1, cy_1, cx_2, cy_2, ex, ey`) and draws a cubic Bezier curve.
+**Q** takes one control point followed by the endpoint (:math:`cx, cy, ex, ey`) and
+draws a quadratic Bezier curve.  Both commands are tessellated into line segments
+at render time and integrate with the normal fill/stroke pipeline, so **-G** and **-W**
+apply as usual.  Use **B** when converting SVG paths (SVG ``C``/``c`` maps directly);
+use **Q** for simpler arcs where one control point is sufficient.
+
 Note for **O**\: if an **a** is appended to the angle then :math:`\alpha` is considered
 to be a map azimuth; otherwise it is a Cartesian map angle.  The **a** modifier
 does not apply if the angle is given via a variable, in which case the type of angle

share/custom/heart.def

@@ -0,0 +1,10 @@
+# Heart shape using cubic Bezier curves (B command)
+# Classic heart: two cubic bezier lobes meeting at bottom tip (0,-0.5)
+# and top center notch (0, 0.15)
+
+# Right lobe: from notch (0,0.15) → top-right → right → bottom tip
+0.0   0.15  M
+ 0.5   0.5  0.5  -0.1  0.0  -0.5  B
+
+# Left lobe: from bottom tip (0,-0.5) → left → top-left → back to notch
+-0.5  -0.1  -0.5   0.5  0.0   0.15  B

share/custom/leaf.def

@@ -0,0 +1,8 @@
+# Leaf shape using quadratic Bezier curves
+# Tip at bottom (0,-0.5), apex at top (0,0.5)
+# Right lobe: cp=(0.5,-0.2), right side curves out
+# Left lobe:  cp=(-0.5,-0.2), symmetric
+
+0.0  -0.5  M
+ 0.5  0.3  0.0  0.5  Q
+-0.5  0.3  0.0 -0.5  Q

src/gmt_plot.c

@@ -7727,6 +7727,22 @@ int gmt_draw_custom_symbol (struct GMT_CTRL *GMT, double x0, double y0, double s
 				gmt_M_free (GMT, yp);
 				break;
 
+			case GMT_SYMBOL_QUAD_BEZIER: {	/* Quadratic Bezier: cp=(x,y) endpoint=(dim[0],dim[1]) */
+				/* P0 = last path point, P1 = (x,y) [control], P2 = (dim[0],dim[1]) [endpoint] */
+				double t, mt, x0b = 0.0, y0b = 0.0;
+				flush = true;
+				if (n > 0) { x0b = xx[n-1]; y0b = yy[n-1]; }
+				for (i = 1; i <= GMT_BEZIER_NPTS; i++) {
+					t = (double)i / GMT_BEZIER_NPTS;
+					mt = 1.0 - t;
+					if (n >= n_alloc) gmt_M_malloc2 (GMT, xx, yy, n, &n_alloc, double);
+					xx[n] = mt*mt*x0b + 2.0*mt*t*x + t*t*dim[0];
+					yy[n] = mt*mt*y0b + 2.0*mt*t*y + t*t*dim[1];
+					n++;
+				}
+				break;
+			}
+
 			case GMT_SYMBOL_ROTATE:		/* Rotate the symbol coordinate system by a fixed amount */
 				if (flush) gmtplot_flush_symbol_piece (GMT, PSL, xx, yy, &n, &p, &f, this_outline, &flush);
 				PSL_setorigin (PSL, 0.0, 0.0, s->p[0], PSL_FWD);
@@ -7756,6 +7772,23 @@ int gmt_draw_custom_symbol (struct GMT_CTRL *GMT, double x0, double y0, double s
 				if (s->pen) current_pen = s->pen;
 				break;
 
+			case GMT_SYMBOL_CUBIC_BEZIER: {	/* Cubic Bezier (B): cp1=(x,y) cp2=(dim[0],dim[1]) endpoint=(dim[2], p[3]*size) */
+				/* B(t) = (1-t)^3*P0 + 3*(1-t)^2*t*P1 + 3*(1-t)*t^2*P2 + t^3*P3 */
+				double t, mt, mt2, t2, x0b = 0.0, y0b = 0.0;
+				double cx2 = dim[0], cy2 = dim[1], ex = dim[2], ey = s->p[3] * size[0];
+				flush = true;
+				if (n > 0) { x0b = xx[n-1]; y0b = yy[n-1]; }
+				for (i = 1; i <= GMT_BEZIER_NPTS; i++) {
+					t = (double)i / GMT_BEZIER_NPTS;
+					mt = 1.0 - t;  mt2 = mt * mt;  t2 = t * t;
+					if (n >= n_alloc) gmt_M_malloc2(GMT, xx, yy, n, &n_alloc, double);
+					xx[n] = mt2*mt*x0b + 3.0*mt2*t*x   + 3.0*mt*t2*cx2 + t2*t*ex;
+					yy[n] = mt2*mt*y0b + 3.0*mt2*t*y   + 3.0*mt*t2*cy2 + t2*t*ey;
+					n++;
+				}
+				break;
+			}
+
 			case (int)'C':
 				if (gmt_M_compat_check (GMT, 4)) {	/* Warn and purposefully fall through to assign the rest of the statements */
 					GMT_Report (GMT->parent, GMT_MSG_COMPAT, "Circle macro symbol C is deprecated; use c instead\n");

src/gmt_plot.h

@@ -54,13 +54,17 @@
 #define GMT_SYMBOL_GEOVECTOR	((int)'=')
 #define GMT_SYMBOL_VARTEXT	((int)'L')
 #define GMT_SYMBOL_EPS	((int)'P')
+#define GMT_SYMBOL_QUAD_BEZIER	((int)'Q')	/* Quadratic Bezier: cp=(x,y) endpoint=(p[0],p[1]) */
+#define GMT_SYMBOL_CUBIC_BEZIER	((int)'B')	/* Cubic Bezier: cp1=(x,y) cp2=(p[0],p[1]) endpoint=(p[2],p[3]) */
 
 #define GMT_SYMBOL_LINE		0
 #define GMT_SYMBOL_NONE		((int)' ')
 #define GMT_SYMBOL_NOT_SET	((int)'*')
 
 #define GMT_DOT_SIZE 0.005	/* Size of a "dot" on a GMT PS map [in inches] */
 
+#define GMT_BEZIER_NPTS 20	/* Tessellation segments for Bezier curve macro commands */
+
 /*! FRONT symbols */
 
 enum GMT_enum_front {GMT_FRONT_FAULT = 0,

src/gmt_support.c

@@ -5784,6 +5784,20 @@ GMT_LOCAL int gmtsupport_init_custom_symbol (struct GMT_CTRL *GMT, char *in_name
 				if ((s->eps = gmtsupport_load_eps_symbol (GMT, name, path)) == NULL) return GMT_RUNTIME_ERROR;
 				break;
 
+			case GMT_SYMBOL_QUAD_BEZIER:	/* Quadratic Bezier: cx cy ex ey Q */
+				if (last != 4) error++;	/* Need cx cy ex ey + action = 5 cols */
+				s->p[0] = atof (col[2]);	/* endpoint x */
+				s->p[1] = atof (col[3]);	/* endpoint y */
+				break;
+
+			case GMT_SYMBOL_CUBIC_BEZIER:	/* Cubic Bezier: cx1 cy1 cx2 cy2 ex ey C */
+				if (last != 6) error++;	/* Need cx1 cy1 cx2 cy2 ex ey + action = 7 cols */
+				s->p[0] = atof (col[2]);	/* second control point x */
+				s->p[1] = atof (col[3]);	/* second control point y */
+				s->p[2] = atof (col[4]);	/* endpoint x */
+				s->p[3] = atof (col[5]);	/* endpoint y */
+				break;
+
 			default:
 				error++;
 				break;

src/gmt_symbol.h

@@ -82,7 +82,7 @@ struct GMT_REFPOINT {	/* Used to hold items relevant for a reference point */
 	char *args;		/* Text representation of any additional arguments */
 };
 
-#define CUSTOM_SYMBOL_MAXVAR	3	/* So we can check in the code if we exceed this */
+#define CUSTOM_SYMBOL_MAXVAR	4	/* So we can check in the code if we exceed this */
 
 enum gmt_enum_custsymb {
 	GMT_CONST_STRING	= -5,	/* We have a constant string in a conditional test */

test/psxy/bezier_demo_cubic.sh

@@ -0,0 +1,26 @@
+#!/usr/bin/env bash
+#
+# Test C (cubic Bezier) command in custom symbol macro language.
+# Uses share/custom/heart.def (closed heart shape via two C curves)
+# alongside share/custom/leaf.def (Q-based) for visual comparison.
+
+ps=bezier_demo_cubic.ps
+
+gmt psbasemap -R-5/5/-4/4 -JX14c/10c -Ba2f1 -BWeSn+t"Cubic Bezier (C) custom symbol demo" -P -K > $ps
+
+# Hearts in a row, different sizes and colors
+for lon in -4 -2 0 2 4; do
+	echo "$lon  2" | gmt psxy -R -J -Skheart/1.5c -Gred     -W0.5p,darkred -O -K >> $ps
+	echo "$lon  0" | gmt psxy -R -J -Skheart/2.0c -Gtomato  -W0.7p,red     -O -K >> $ps
+	echo "$lon -2" | gmt psxy -R -J -Skheart/2.5c -Gdarkred -W1p,black     -O -K >> $ps
+done
+
+# Compare: leaves (Q) vs hearts (C) side by side
+for lon in -3.5 -1.5 0.5 2.5; do
+	echo "$lon  3.3" | gmt psxy -R -J -Skleaf/1.2c  -Ggreen -W0.5p,darkgreen -O -K >> $ps
+done
+for lon in -2.5 -0.5 1.5 3.5; do
+	echo "$lon  3.3" | gmt psxy -R -J -Skheart/1.2c -Gred   -W0.5p,darkred   -O -K >> $ps
+done
+
+echo "0 3.8 Q (leaf) vs C (heart)" | gmt pstext -R -J -F+f10p,Helvetica-Bold+jCM -O >> $ps

test/psxy/bezier_demo_quadratic.sh

@@ -0,0 +1,31 @@
+#!/usr/bin/env bash
+#
+# Test Q (quadratic Bezier) command in custom symbol macro language.
+# Uses share/custom/leaf.def (closed leaf shape from two Q curves)
+# and share/custom/qbezier_test.def (open parabolic arc).
+
+ps=bezier_demo_quadratic.ps
+
+gmt psbasemap -R-5/5/-4/4 -JX14c/10c -Ba2f1 -BWeSn+t"Quadratic Bezier (Q) custom symbol demo" -P -K > $ps
+
+# Grid of leaves at different sizes and colors
+for lon in -4 -2 0 2 4; do
+	echo "$lon  2" | gmt psxy -R -J -Skleaf/1.5c -Glightgreen -W0.5p,darkgreen -O -K >> $ps
+	echo "$lon  0" | gmt psxy -R -J -Skleaf/2.0c -Ggreen      -W0.7p,darkgreen -O -K >> $ps
+	echo "$lon -2" | gmt psxy -R -J -Skleaf/2.5c -Gdarkgreen  -W1p,black       -O -K >> $ps
+done
+
+# Parabolic arc symbol (open path, just stroked)
+for lon in -3 -1 1 3; do
+	echo "$lon  3.2" | gmt psxy -R -J -Skqbezier_test/1.5c -W1.5p,red -O -K >> $ps
+done
+
+# Labels
+gmt pstext -R -J -F+f11p,Helvetica-Bold,red+jCM -O -K >> $ps << EOF
+0 3.7 Parabolic arcs
+EOF
+gmt pstext -R -J -F+f9p+jCM -O >> $ps << EOF
+0 2.7 1.5c leaves
+0 0.7 2.0c leaves
+0 -1.3 2.5c leaves
+EOF