[freetype2] gsoc-anurag-2023 0f715c8b9 1/2: Add support for conics

[Werner Lemberg]

branch: gsoc-anurag-2023
commit 0f715c8b90dbe549f9aeacbe8c4c26555bb7973d
Author: Anurag Thakur <anurag105csec21@bpitindia.edu.in>
Commit: Anurag Thakur <anurag105csec21@bpitindia.edu.in>

    Add support for conics
---
 src/base/ftobjs.c | 160 ++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 160 insertions(+)

diff --git a/src/base/ftobjs.c b/src/base/ftobjs.c
index e3b32fa7c..747d0cb1f 100644
--- a/src/base/ftobjs.c
+++ b/src/base/ftobjs.c
@@ -2543,6 +2543,98 @@
 
 
 
+static FT_Vector
+Lerp( float T, FT_Vector P0, FT_Vector P1 )
+{
+  FT_Vector p;
+  p.x = P0.x + T * ( P1.x - P0.x );
+  p.y = P0.y + T * ( P1.y - P0.y );
+  return p;
+}
+
+int conic_to2(FT_GlyphSlot* slot, FT_Vector *control, FT_Vector *from, 
FT_Vector *to, FT_PreLine *ptr)
+{
+  /*
+  Calculate devsq as the square of four times the
+  distance from the control point to the midpoint of the curve.
+  This is the place at which the curve is furthest from the
+  line joining the control points.
+
+  4 x point on curve = p0 + 2p1 + p2
+  4 x midpoint = 4p1
+
+  The division by four is omitted to save time.
+  */
+  //FT_PreLine ptr = (*slot)->prelines;
+  if((*slot)->glyph_index == 38)
+  printf("conic from %d, %d to %d, %d via %d, %d\n", from->x, from->y, to->x, 
to->y, control->x, control->y);
+  FT_Vector aP0 = { from->x , from->y};
+  FT_Vector aP1 = { control->x, control->y };
+  FT_Vector aP2 = { to->x, to->y };
+
+  float devx  = aP0.x - aP1.x - aP1.x + aP2.x;
+  float devy  = aP0.y - aP1.y - aP1.y + aP2.y;
+  float devsq = devx * devx + devy * devy;
+
+  if ( devsq < 0.333f )
+  {
+    //dense_line_to( &aP2, worker );
+    FT_PreLine pl3  = malloc(sizeof(FT_PreLineRec));
+            pl3->x1 = (*ptr)->x2;
+            pl3->y1 = (*ptr)->y2;
+            pl3->x2 = aP2.x;
+            pl3->y2 = aP2.y;
+            pl3->next = NULL;
+            pl3->ismove = 0;
+            (*ptr)->next = pl3;
+            *ptr = (*ptr)->next;
+    return;
+  }
+
+  /*
+  According to Raph Levien, the reason for the subdivision by n (instead of
+  recursive division by the Casteljau system) is that "I expect the flatness
+  computation to be semi-expensive (it's done once rather than on each 
potential
+  subdivision) and also because you'll often get fewer subdivisions. Taking a
+  circular arc as a simplifying assumption, where I get n, a recursive approach
+  would get 2^ceil(lg n), which, if I haven't made any horrible mistakes, is
+  expected to be 33% more in the limit".
+  */
+
+  const float tol = 3.0f;
+  int         n   = (int)floor( sqrt( sqrt( tol * devsq ) ) )/8;
+  FT_Vector p      = aP0;
+  float     nrecip = 1.0f / ( n + 1.0f );
+  float     t      = 0.0f;
+  for ( int i = 0; i < n; i++ )
+  {
+    t += nrecip;
+    FT_Vector next = Lerp( t, Lerp( t, aP0, aP1 ), Lerp( t, aP1, aP2 ) );
+    //dense_line_to(&next, worker );
+    FT_PreLine pl4  = malloc(sizeof(FT_PreLineRec));
+            pl4->x1 = (*ptr)->x2;
+            pl4->y1 = (*ptr)->y2;
+            pl4->x2 = next.x;
+            pl4->y2 = next.y;
+            pl4->next = NULL;
+            pl4->ismove = 0;
+            (*ptr)->next = pl4;
+            *ptr = (*ptr)->next;
+    p              = next;
+  }
+
+  //dense_line_to( &aP2, worker );
+  FT_PreLine pl5  = malloc(sizeof(FT_PreLineRec));
+            pl5->x1 = (*ptr)->x2;
+            pl5->y1 = (*ptr)->y2;
+            pl5->x2 = aP2.x;
+            pl5->y2 = aP2.y;
+            pl5->next = NULL;
+            pl5->ismove = 0;
+            (*ptr)->next = pl5;
+            *ptr = (*ptr)->next;
+
+}
 
 
   static FT_Error ft_decompose_outline(FT_GlyphSlot* slot){
@@ -2688,6 +2780,74 @@
             ptr = ptr->next;
             continue;
           }
+        
+        case FT_CURVE_TAG_CONIC:  /* consume conic arcs */
+          // v_control.x = SCALED( point->x );
+          // v_control.y = SCALED( point->y );
+
+        Do_Conic:
+          if ( point < limit )
+          {
+            FT_Vector  vec;
+            FT_Vector  v_middle;
+
+
+            point++;
+            tags++;
+            tag = FT_CURVE_TAG( tags[0] );
+
+            // vec.x = SCALED( point->x );
+            // vec.y = SCALED( point->y );
+            vec.x = point->x;
+            vec.y = point->y;
+
+            if ( tag == FT_CURVE_TAG_ON )
+            {
+              FT_TRACE5(( "  conic to (%.2f, %.2f)"
+                          " with control (%.2f, %.2f)\n",
+                          (double)vec.x / 64,
+                          (double)vec.y / 64,
+                          (double)v_control.x / 64,
+                          (double)v_control.y / 64 ));
+              FT_Vector vex0 = {ptr->x2, ptr->y2};
+              error = conic_to2(slot, &v_control, &vex0,&vec , &ptr);
+              // if ( error )
+              //   goto Exit;
+              continue;
+            }
+
+            if ( tag != FT_CURVE_TAG_CONIC )
+            {
+              FT_TRACE5( ( "Invalid Outline" ) );
+              break;
+            }
+            v_middle.x = ( v_control.x + vec.x ) / 2;
+            v_middle.y = ( v_control.y + vec.y ) / 2;
+
+            FT_TRACE5(( "  conic to (%.2f, %.2f)"
+                        " with control (%.2f, %.2f)\n",
+                        (double)v_middle.x / 64,
+                        (double)v_middle.y / 64,
+                        (double)v_control.x / 64,
+                        (double)v_control.y / 64 ));
+            FT_Vector vex = {ptr->x2, ptr->y2};
+            error = conic_to2(slot, &v_control, &vex,&v_middle, &ptr);
+            // if ( error )
+            //   goto Exit;
+
+            v_control = vec;
+            goto Do_Conic;
+          }
+
+          FT_TRACE5(( "  conic to (%.2f, %.2f)"
+                      " with control (%.2f, %.2f)\n",
+                      (double)v_start.x / 64,
+                      (double)v_start.y / 64,
+                      (double)v_control.x / 64,
+                      (double)v_control.y / 64 ));
+          FT_Vector vex2 = {ptr->x2, ptr->y2};
+          error = conic_to2( slot, &v_control, &vex2, &v_start, &ptr );
+          //goto Close;
 
         }
       }