Bezier curve functions

meson.build

@@ -238,6 +238,7 @@ config.set('TAISEI_BUILDCONF_HAVE_INT128', cc.sizeof('__int128') == 16)
 config.set('TAISEI_BUILDCONF_HAVE_LONG_DOUBLE', cc.sizeof('long double') > 8)
 config.set('TAISEI_BUILDCONF_HAVE_POSIX', have_posix)
 config.set('TAISEI_BUILDCONF_HAVE_SINCOS', cc.has_function('sincos', dependencies : dep_m))
+config.set('TAISEI_BUILDCONF_HAVE_SINCOSF', cc.has_function('sincosf', dependencies : dep_m))
 
 if config.get('TAISEI_BUILDCONF_HAVE_SINCOS')
     config.set('_GNU_SOURCE', true)

src/util/bezier.c

@@ -0,0 +1,66 @@
+/*
+ * This software is licensed under the terms of the MIT License.
+ * See COPYING for further information.
+ * ---
+ * Copyright (c) 2011-2019, Lukas Weber <[email protected]>.
+ * Copyright (c) 2012-2019, Andrei Alexeyev <[email protected]>.
+*/
+
+#include "taisei.h"
+
+#include "bezier.h"
+#include "miscmath.h"
+
+cmplxf cbezier_point_at(CubicBezier curve, float t) {
+	float u = 1.0f - t;
+	float uu = u * u;
+	float tt = t * t;
+	float uuu = uu * u;
+	float uut3 = uu * t * 3.0f;
+	float utt3 = u * tt * 3.0f;
+	float ttt = tt * t;
+
+	return
+		curve.points[0] * uuu +
+		curve.points[1] * uut3 +
+		curve.points[2] * utt3 +
+		curve.points[3] * ttt;
+}
+
+cmplxf cbezier_derivative_at(CubicBezier curve, float t) {
+	float u = 1.0f - t;
+
+	return
+		(curve.points[1] - curve.points[0]) * (3.0f * u * u) +
+		(curve.points[2] - curve.points[1]) * (6.0f * u * t) +
+		(curve.points[3] - curve.points[2]) * (3.0f * t * t);
+}
+
+cmplxf cbezier_derivative2_at(CubicBezier curve, float t) {
+	float t6 = 6.0f * t;
+	float u6 = 6.0f - t6;
+
+	return
+		(curve.points[2] - 2.0f * curve.points[1] + curve.points[0]) * u6 +
+		(curve.points[3] - 2.0f * curve.points[2] + curve.points[1]) * t6;
+}
+
+void cbezier_scale(CubicBezier *curve, cmplxf x) {
+	curve->points[0] *= x;
+	curve->points[1] *= x;
+	curve->points[2] *= x;
+	curve->points[3] *= x;
+}
+
+void cbezier_translate(CubicBezier *curve, cmplxf x) {
+	curve->points[0] += x;
+	curve->points[1] += x;
+	curve->points[2] += x;
+	curve->points[3] += x;
+}
+
+void cbezier_rotate(CubicBezier *curve, cmplxf pivot, float angle) {
+	cbezier_translate(curve, -pivot);
+	cbezier_scale(curve, cdirf(angle));
+	cbezier_translate(curve, pivot);
+}

src/util/bezier.h

@@ -0,0 +1,31 @@
+/*
+ * This software is licensed under the terms of the MIT License.
+ * See COPYING for further information.
+ * ---
+ * Copyright (c) 2011-2019, Lukas Weber <[email protected]>.
+ * Copyright (c) 2012-2019, Andrei Alexeyev <[email protected]>.
+*/
+
+#ifndef IGUARD_util_bezier_h
+#define IGUARD_util_bezier_h
+
+#include "taisei.h"
+
+typedef union CubicBezier {
+	struct {
+		cmplxf start, control[2], end;
+	};
+	struct {
+		cmplxf points[4];
+	};
+} CubicBezier;
+
+cmplxf cbezier_point_at(CubicBezier curve, float t) attr_const;
+cmplxf cbezier_derivative_at(CubicBezier curve, float t) attr_const;
+cmplxf cbezier_derivative2_at(CubicBezier curve, float t) attr_const;
+
+void cbezier_scale(CubicBezier *curve, cmplxf x);
+void cbezier_translate(CubicBezier *curve, cmplxf x);
+void cbezier_rotate(CubicBezier *curve, cmplxf pivot, float angle);
+
+#endif // IGUARD_util_bezier_h

src/util/meson.build

@@ -3,6 +3,7 @@ util_deps = []
 
 util_src = files(
     'assert.c',
+    'bezier.c',
     'crap.c',
     'env.c',
     'fbmgr.c',

src/util/miscmath.c

@@ -134,6 +134,18 @@ cmplx cdir(double angle) {
 	#endif
 }
 
+cmplxf cdirf(float angle) {
+	// this is faster than cexp(I*angle)
+
+	#ifdef TAISEI_BUILDCONF_HAVE_SINCOSF
+	float s, c;
+	sincosf(angle, &s, &c);
+	return CMPLXF(c, s);
+	#else
+	return CMPLXF(cosf(angle), sinf(angle));
+	#endif
+}
+
 cmplx cwmul(cmplx c0, cmplx c1) {
 	return CMPLX(creal(c0)*creal(c1), cimag(c0)*cimag(c1));
 }

src/util/miscmath.h

@@ -42,6 +42,7 @@ cmplx cnormalize(cmplx c) attr_const;
 cmplx cclampabs(cmplx c, double maxabs) attr_const;
 cmplx cwclamp(cmplx c, cmplx cmin, cmplx cmax) attr_const;
 cmplx cdir(double angle) attr_const;
+cmplxf cdirf(float angle) attr_const;
 cmplx cwmul(cmplx c0, cmplx c1) attr_const;
 cmplxf cwmulf(cmplxf c0, cmplxf c1) attr_const;
 cmplx cswap(cmplx c) attr_const;