common math: code refactoring

introduce common math functions to improve the reusability.

src/lib/meson.build

@@ -17,6 +17,7 @@ source_file = [
    'tvgLoader.h',
    'tvgLoadModule.h',
    'tvgLzw.h',
+   'tvgMath.h',
    'tvgPictureImpl.h',
    'tvgRender.h',
    'tvgIteratorAccessor.h',

src/lib/sw_engine/tvgSwCommon.h

@@ -299,9 +299,6 @@ bool mathSmallCubic(const SwPoint* base, SwFixed& angleIn, SwFixed& angleMid, Sw
 SwFixed mathMean(SwFixed angle1, SwFixed angle2);
 SwPoint mathTransform(const Point* to, const Matrix* transform);
 bool mathUpdateOutlineBBox(const SwOutline* outline, const SwBBox& clipRegion, SwBBox& renderRegion, bool fastTrack);
-bool mathInverse(const Matrix* m, Matrix* invM);
-bool mathMultiply(const Matrix* lhs, Matrix* rhs);
-bool mathIdentity(const Matrix* m);
 
 void shapeReset(SwShape* shape);
 bool shapePrepare(SwShape* shape, const Shape* sdata, const Matrix* transform, const SwBBox& clipRegion, SwBBox& renderRegion, SwMpool* mpool, unsigned tid, bool hasComposite);

src/lib/sw_engine/tvgSwFill.cpp

@@ -19,8 +19,7 @@
  * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  * SOFTWARE.
  */
-#include <float.h>
+#include "tvgMath.h"
-#include <math.h>
 #include "tvgSwCommon.h"
 
 
@@ -117,10 +116,10 @@ bool _prepareLinear(SwFill* fill, const LinearGradient* linear, const Matrix* tr
     fill->linear.offset = -fill->linear.dx * x1 - fill->linear.dy * y1;
 
     auto gradTransform = linear->transform();
-    bool isTransformation = !mathIdentity(&gradTransform);
+    bool isTransformation = !mathIdentity((const Matrix*)(&gradTransform));
 
     if (isTransformation) {
-        if (transform) mathMultiply(transform, &gradTransform);
+        if (transform) gradTransform = mathMultiply(transform, &gradTransform);
     } else if (transform) {
         gradTransform = *transform;
         isTransformation = true;
@@ -156,10 +155,10 @@ bool _prepareRadial(SwFill* fill, const RadialGradient* radial, const Matrix* tr
     fill->radial.a = radius;
 
     auto gradTransform = radial->transform();
-    bool isTransformation = !mathIdentity(&gradTransform);
+    bool isTransformation = !mathIdentity((const Matrix*)(&gradTransform));
 
     if (isTransformation) {
-        if (transform) mathMultiply(transform, &gradTransform);
+        if (transform) gradTransform = mathMultiply(transform, &gradTransform);
     } else if (transform) {
         gradTransform = *transform;
         isTransformation = true;

src/lib/sw_engine/tvgSwMath.cpp

@@ -20,7 +20,6 @@
  * SOFTWARE.
  */
 #include <math.h>
-#include <float.h>
 #include "tvgSwCommon.h"
 
 
@@ -497,63 +496,3 @@ bool mathUpdateOutlineBBox(const SwOutline* outline, const SwBBox& clipRegion, S
 
     return true;
 }
-
-
-bool mathInverse(const Matrix* m, Matrix* invM)
-{
-    auto det = m->e11 * (m->e22 * m->e33 - m->e32 * m->e23) -
-               m->e12 * (m->e21 * m->e33 - m->e23 * m->e31) +
-               m->e13 * (m->e21 * m->e32 - m->e22 * m->e31);
-
-    if (fabsf(det) < FLT_EPSILON) return false;
-
-    auto invDet = 1 / det;
-
-    invM->e11 = (m->e22 * m->e33 - m->e32 * m->e23) * invDet;
-    invM->e12 = (m->e13 * m->e32 - m->e12 * m->e33) * invDet;
-    invM->e13 = (m->e12 * m->e23 - m->e13 * m->e22) * invDet;
-    invM->e21 = (m->e23 * m->e31 - m->e21 * m->e33) * invDet;
-    invM->e22 = (m->e11 * m->e33 - m->e13 * m->e31) * invDet;
-    invM->e23 = (m->e21 * m->e13 - m->e11 * m->e23) * invDet;
-    invM->e31 = (m->e21 * m->e32 - m->e31 * m->e22) * invDet;
-    invM->e32 = (m->e31 * m->e12 - m->e11 * m->e32) * invDet;
-    invM->e33 = (m->e11 * m->e22 - m->e21 * m->e12) * invDet;
-
-    return true;
-}
-
-
-bool mathMultiply(const Matrix* lhs, Matrix* rhs)
-{
-    Matrix m;
-
-    m.e11 = lhs->e11 * rhs->e11 + lhs->e12 * rhs->e21 + lhs->e13 * rhs->e31;
-    m.e12 = lhs->e11 * rhs->e12 + lhs->e12 * rhs->e22 + lhs->e13 * rhs->e32;
-    m.e13 = lhs->e11 * rhs->e13 + lhs->e12 * rhs->e23 + lhs->e13 * rhs->e33;
-
-    m.e21 = lhs->e21 * rhs->e11 + lhs->e22 * rhs->e21 + lhs->e23 * rhs->e31;
-    m.e22 = lhs->e21 * rhs->e12 + lhs->e22 * rhs->e22 + lhs->e23 * rhs->e32;
-    m.e23 = lhs->e21 * rhs->e13 + lhs->e22 * rhs->e23 + lhs->e23 * rhs->e33;
-
-    m.e31 = lhs->e31 * rhs->e11 + lhs->e32 * rhs->e21 + lhs->e33 * rhs->e31;
-    m.e32 = lhs->e31 * rhs->e12 + lhs->e32 * rhs->e22 + lhs->e33 * rhs->e32;
-    m.e33 = lhs->e31 * rhs->e13 + lhs->e32 * rhs->e23 + lhs->e33 * rhs->e33;
-
-    *rhs = m;
-
-    return true;
-}
-
-
-bool mathIdentity(const Matrix* m)
-{
-    if (m) {
-        if (m->e11 != 1.0f || m->e12 != 0.0f || m->e13 != 0.0f ||
-            m->e21 != 0.0f || m->e22 != 1.0f || m->e23 != 0.0f ||
-            m->e31 != 0.0f || m->e32 != 0.0f || m->e33 != 1.0f) {
-            return false;
-        }
-    }
-
-    return true;
-}

src/lib/sw_engine/tvgSwRaster.cpp

@@ -19,10 +19,9 @@
  * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  * SOFTWARE.
  */
-#include <float.h>
+#include "tvgMath.h"
-#include <math.h>
-#include "tvgSwCommon.h"
 #include "tvgRender.h"
+#include "tvgSwCommon.h"
 #include "tvgSwRasterC.h"
 #include "tvgSwRasterAvx.h"
 #include "tvgSwRasterNeon.h"

src/lib/tvgMath.h

@@ -0,0 +1,139 @@
+/*
+ * Copyright (c) 2021 Samsung Electronics Co., Ltd. All rights reserved.
+
+ * Permission is hereby granted, free of charge, to any person obtaining a copy
+ * of this software and associated documentation files (the "Software"), to deal
+ * in the Software without restriction, including without limitation the rights
+ * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+ * copies of the Software, and to permit persons to whom the Software is
+ * furnished to do so, subject to the following conditions:
+
+ * The above copyright notice and this permission notice shall be included in all
+ * copies or substantial portions of the Software.
+
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+ * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+#ifndef _TVG_MATH_H_
+#define _TVG_MATH_H_
+
+ #define _USE_MATH_DEFINES
+
+#include <float.h>
+#include <math.h>
+#include "tvgCommon.h"
+
+
+static inline bool mathIdentity(const Matrix* m)
+{
+    if (m) {
+        if (fabs(m->e11 - 1) > FLT_EPSILON || fabs(m->e12) > FLT_EPSILON || fabs(m->e13) > FLT_EPSILON ||
+            fabs(m->e21) > FLT_EPSILON || fabs(m->e22 - 1) > FLT_EPSILON || fabs(m->e23) > FLT_EPSILON ||
+            fabs(m->e31) > FLT_EPSILON || fabs(m->e32) > FLT_EPSILON || fabs(m->e33 - 1) > FLT_EPSILON) {
+            return false;
+        }
+    }
+    return true;
+}
+
+
+static inline bool mathInverse(const Matrix* m, Matrix* out)
+{
+    auto det = m->e11 * (m->e22 * m->e33 - m->e32 * m->e23) -
+               m->e12 * (m->e21 * m->e33 - m->e23 * m->e31) +
+               m->e13 * (m->e21 * m->e32 - m->e22 * m->e31);
+
+    if (fabsf(det) < FLT_EPSILON) return false;
+
+    auto invDet = 1 / det;
+
+    out->e11 = (m->e22 * m->e33 - m->e32 * m->e23) * invDet;
+    out->e12 = (m->e13 * m->e32 - m->e12 * m->e33) * invDet;
+    out->e13 = (m->e12 * m->e23 - m->e13 * m->e22) * invDet;
+    out->e21 = (m->e23 * m->e31 - m->e21 * m->e33) * invDet;
+    out->e22 = (m->e11 * m->e33 - m->e13 * m->e31) * invDet;
+    out->e23 = (m->e21 * m->e13 - m->e11 * m->e23) * invDet;
+    out->e31 = (m->e21 * m->e32 - m->e31 * m->e22) * invDet;
+    out->e32 = (m->e31 * m->e12 - m->e11 * m->e32) * invDet;
+    out->e33 = (m->e11 * m->e22 - m->e21 * m->e12) * invDet;
+
+    return true;
+}
+
+
+static inline void mathIdentity(Matrix* m)
+{
+    m->e11 = 1.0f;
+    m->e12 = 0.0f;
+    m->e13 = 0.0f;
+    m->e21 = 0.0f;
+    m->e22 = 1.0f;
+    m->e23 = 0.0f;
+    m->e31 = 0.0f;
+    m->e32 = 0.0f;
+    m->e33 = 1.0f;
+}
+
+
+static inline void mathScale(Matrix* m, float scale)
+{
+    m->e11 = scale;
+    m->e22 = scale;
+}
+
+
+static inline void mathTranslate(Matrix* m, float x, float y)
+{
+    m->e13 = x;
+    m->e23 = y;   
+}
+
+
+static inline void mathRotate(Matrix* m, float degree)
+{
+    auto radian = degree / 180.0f * M_PI;
+    auto cosVal = cosf(radian);
+    auto sinVal = sinf(radian);
+
+    m->e12 = m->e11 * -sinVal;
+    m->e11 *= cosVal;
+    m->e21 = m->e22 * sinVal;
+    m->e22 *= cosVal;
+}
+
+
+static inline void mathMultiply(Point* pt, const Matrix* transform)
+{
+    auto tx = pt->x * transform->e11 + pt->y * transform->e12 + transform->e13;
+    auto ty = pt->x * transform->e21 + pt->y * transform->e22 + transform->e23;
+    pt->x = tx;
+    pt->y = ty;
+}
+
+
+static inline Matrix mathMultiply(const Matrix* lhs, const Matrix* rhs)
+{
+    Matrix m;
+
+    m.e11 = lhs->e11 * rhs->e11 + lhs->e12 * rhs->e21 + lhs->e13 * rhs->e31;
+    m.e12 = lhs->e11 * rhs->e12 + lhs->e12 * rhs->e22 + lhs->e13 * rhs->e32;
+    m.e13 = lhs->e11 * rhs->e13 + lhs->e12 * rhs->e23 + lhs->e13 * rhs->e33;
+
+    m.e21 = lhs->e21 * rhs->e11 + lhs->e22 * rhs->e21 + lhs->e23 * rhs->e31;
+    m.e22 = lhs->e21 * rhs->e12 + lhs->e22 * rhs->e22 + lhs->e23 * rhs->e32;
+    m.e23 = lhs->e21 * rhs->e13 + lhs->e22 * rhs->e23 + lhs->e23 * rhs->e33;
+
+    m.e31 = lhs->e31 * rhs->e11 + lhs->e32 * rhs->e21 + lhs->e33 * rhs->e31;
+    m.e32 = lhs->e31 * rhs->e12 + lhs->e32 * rhs->e22 + lhs->e33 * rhs->e32;
+    m.e33 = lhs->e31 * rhs->e13 + lhs->e32 * rhs->e23 + lhs->e33 * rhs->e33;
+
+    return m;
+}
+
+
+#endif //_TVG_MATH_H_

src/lib/tvgPaint.cpp

@@ -21,6 +21,7 @@
  */
 #include <float.h>
 #include <math.h>
+#include "tvgMath.h"
 #include "tvgPaint.h"
 
 /************************************************************************/
@@ -261,17 +262,9 @@ bool Paint::Impl::bounds(float* x, float* y, float* w, float* h, bool transforme
     auto x2 = -FLT_MAX;
     auto y2 = -FLT_MAX;
 
-    //function = Point * Matrix
-    auto multiply = [&](Point* pt, const Matrix* transform) {
-        auto tx = pt->x * transform->e11 + pt->y * transform->e12 + transform->e13;
-        auto ty = pt->x * transform->e21 + pt->y * transform->e22 + transform->e23;
-        pt->x = tx;
-        pt->y = ty;
-    };
-
     //Compute the AABB after transformation
     for (int i = 0; i < 4; i++) {
-        multiply(&pt[i], m);
+        mathMultiply(&pt[i], m);
 
         if (pt[i].x < x1) x1 = pt[i].x;
         if (pt[i].x > x2) x2 = pt[i].x;

src/lib/tvgRender.cpp

@@ -19,8 +19,7 @@
  * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  * SOFTWARE.
  */
-#include <float.h>
+#include "tvgMath.h"
-#include <math.h>
 #include "tvgRender.h"
 
 /************************************************************************/
@@ -46,8 +45,6 @@ void RenderTransform::override(const Matrix& m)
 
 bool RenderTransform::update()
 {
-    constexpr auto PI = 3.141592f;
-
     if (overriding) return true;
 
     //Init Status
@@ -56,35 +53,13 @@ bool RenderTransform::update()
         return false;
     }
 
-    //identity
+    mathIdentity(&m);
-    m.e11 = 1.0f;
-    m.e12 = 0.0f;
-    m.e13 = 0.0f;
-    m.e21 = 0.0f;
-    m.e22 = 1.0f;
-    m.e23 = 0.0f;
-    m.e31 = 0.0f;
-    m.e32 = 0.0f;
-    m.e33 = 1.0f;
 
-    //scale
+    mathScale(&m, scale);
-    m.e11 = scale;
-    m.e22 = scale;
 
-    //rotation
+    if (fabsf(degree) > FLT_EPSILON) mathRotate(&m, degree);
-    if (fabsf(degree) > FLT_EPSILON) {
-        auto radian = degree / 180.0f * PI;
-        auto cosVal = cosf(radian);
-        auto sinVal = sinf(radian);
 
-        m.e12 = m.e11 * -sinVal;
+    mathTranslate(&m, x, y);
-        m.e11 *= cosVal;
-        m.e21 = m.e22 * sinVal;
-        m.e22 *= cosVal;
-    }
-
-    m.e13 = x;
-    m.e23 = y;
 
     return true;
 }
@@ -97,15 +72,5 @@ RenderTransform::RenderTransform()
 
 RenderTransform::RenderTransform(const RenderTransform* lhs, const RenderTransform* rhs)
 {
-    m.e11 = lhs->m.e11 * rhs->m.e11 + lhs->m.e12 * rhs->m.e21 + lhs->m.e13 * rhs->m.e31;
+    m = mathMultiply(&lhs->m, &rhs->m);
-    m.e12 = lhs->m.e11 * rhs->m.e12 + lhs->m.e12 * rhs->m.e22 + lhs->m.e13 * rhs->m.e32;
-    m.e13 = lhs->m.e11 * rhs->m.e13 + lhs->m.e12 * rhs->m.e23 + lhs->m.e13 * rhs->m.e33;
-
-    m.e21 = lhs->m.e21 * rhs->m.e11 + lhs->m.e22 * rhs->m.e21 + lhs->m.e23 * rhs->m.e31;
-    m.e22 = lhs->m.e21 * rhs->m.e12 + lhs->m.e22 * rhs->m.e22 + lhs->m.e23 * rhs->m.e32;
-    m.e23 = lhs->m.e21 * rhs->m.e13 + lhs->m.e22 * rhs->m.e23 + lhs->m.e23 * rhs->m.e33;
-
-    m.e31 = lhs->m.e31 * rhs->m.e11 + lhs->m.e32 * rhs->m.e21 + lhs->m.e33 * rhs->m.e31;
-    m.e32 = lhs->m.e31 * rhs->m.e12 + lhs->m.e32 * rhs->m.e22 + lhs->m.e33 * rhs->m.e32;
-    m.e33 = lhs->m.e31 * rhs->m.e13 + lhs->m.e32 * rhs->m.e23 + lhs->m.e33 * rhs->m.e33;
 }

src/savers/tvg/tvgTvgSaver.cpp

@@ -19,8 +19,7 @@
  * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  * SOFTWARE.
  */
-#include <float.h>
+#include "tvgMath.h"
-#include <math.h>
 #include "tvgSaveModule.h"
 #include "tvgTvgSaver.h"
 #include "tvgLzw.h"
@@ -57,35 +56,6 @@ static inline TvgBinCounter SERIAL_DONE(TvgBinCounter cnt)
 }
 
 
-static Matrix _multiply(const Matrix* lhs, const Matrix* rhs)
-{
-    Matrix m;
-
-    m.e11 = lhs->e11 * rhs->e11 + lhs->e12 * rhs->e21 + lhs->e13 * rhs->e31;
-    m.e12 = lhs->e11 * rhs->e12 + lhs->e12 * rhs->e22 + lhs->e13 * rhs->e32;
-    m.e13 = lhs->e11 * rhs->e13 + lhs->e12 * rhs->e23 + lhs->e13 * rhs->e33;
-
-    m.e21 = lhs->e21 * rhs->e11 + lhs->e22 * rhs->e21 + lhs->e23 * rhs->e31;
-    m.e22 = lhs->e21 * rhs->e12 + lhs->e22 * rhs->e22 + lhs->e23 * rhs->e32;
-    m.e23 = lhs->e21 * rhs->e13 + lhs->e22 * rhs->e23 + lhs->e23 * rhs->e33;
-
-    m.e31 = lhs->e31 * rhs->e11 + lhs->e32 * rhs->e21 + lhs->e33 * rhs->e31;
-    m.e32 = lhs->e31 * rhs->e12 + lhs->e32 * rhs->e22 + lhs->e33 * rhs->e32;
-    m.e33 = lhs->e31 * rhs->e13 + lhs->e32 * rhs->e23 + lhs->e33 * rhs->e33;
-
-    return m;
-}
-
-
-static void _multiply(Point* pt, const Matrix* transform)
-{
-    auto tx = pt->x * transform->e11 + pt->y * transform->e12 + transform->e13;
-    auto ty = pt->x * transform->e21 + pt->y * transform->e22 + transform->e23;
-    pt->x = tx;
-    pt->y = ty;
-}
-
-
 /* if the properties are identical, we can merge the shapes. */
 static bool _merge(Shape* from, Shape* to)
 {
@@ -325,11 +295,7 @@ TvgBinCounter TvgSaver::writeTagProperty(TvgBinTag tag, TvgBinCounter cnt, const
 
 TvgBinCounter TvgSaver::writeTransform(const Matrix* transform, TvgBinTag tag)
 {
-    if (fabs(transform->e11 - 1) > FLT_EPSILON || fabs(transform->e12) > FLT_EPSILON || fabs(transform->e13) > FLT_EPSILON ||
+    if (!mathIdentity(transform)) return writeTagProperty(tag, SIZE(Matrix), transform);
-        fabs(transform->e21) > FLT_EPSILON || fabs(transform->e22 - 1) > FLT_EPSILON || fabs(transform->e23) > FLT_EPSILON ||
-        fabs(transform->e31) > FLT_EPSILON || fabs(transform->e32) > FLT_EPSILON || fabs(transform->e33 - 1) > FLT_EPSILON) {
-        return writeTagProperty(tag, SIZE(Matrix), transform);
-    }
     return 0;
 }
 
@@ -451,7 +417,8 @@ TvgBinCounter TvgSaver::serializeFill(const Fill* fill, TvgBinTag tag, const Mat
     cnt += writeTagProperty(TVG_TAG_FILL_COLORSTOPS, stopsCnt * SIZE(Fill::ColorStop), stops);
 
     auto gTransform = fill->transform();
-    if (pTransform) gTransform = _multiply(pTransform, &gTransform);
+    if (pTransform) gTransform = mathMultiply(pTransform, &gTransform);
+
     cnt += writeTransform(&gTransform, TVG_TAG_FILL_TRANSFORM);
 
     writeReservedCount(cnt);
@@ -536,7 +503,7 @@ TvgBinCounter TvgSaver::serializePath(const Shape* shape, const Matrix* transfor
             fabs(transform->e21) > FLT_EPSILON || fabs(transform->e22 - 1) > FLT_EPSILON || fabs(transform->e23) > FLT_EPSILON ||
             fabs(transform->e31) > FLT_EPSILON || fabs(transform->e32) > FLT_EPSILON || fabs(transform->e33 - 1) > FLT_EPSILON) {
             auto p = const_cast<Point*>(pts);
-            for (uint32_t i = 0; i < ptsCnt; ++i) _multiply(p++, transform);
+            for (uint32_t i = 0; i < ptsCnt; ++i) mathMultiply(p++, transform);
         }
     }
 
@@ -710,7 +677,7 @@ TvgBinCounter TvgSaver::serialize(const Paint* paint, const Matrix* pTransform,
     if (!compTarget && paint->opacity() == 0) return 0;
 
     auto transform = const_cast<Paint*>(paint)->transform();
-    if (pTransform) transform = _multiply(pTransform, &transform);
+    if (pTransform) transform = mathMultiply(pTransform, &transform);
 
     switch (paint->identifier()) {
         case TVG_CLASS_ID_SHAPE: return serializeShape(static_cast<const Shape*>(paint), pTransform, &transform);