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ovalRasterizer.cpp
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ovalRasterizer.cpp
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/** ---------------------------------------------------------------------------
*
* \file ovalRasterizer.h
* \description This file contains the code that will raterize oval shapes
* into a frame buffer
---------------------------------------------------------------------------- */
#include "ovalRasterizer.h"
#include <algorithm>
#include <cassert>
#include <cmath>
#include <iso646.h>
#include <set>
#ifdef TESTING
#include <doctest/doctest.h>
#endif
struct floatBounds
{
float left;
float top;
float right;
float bottom;
void add( const floatBounds& other )
{
left = std::min( left, other.left );
top = std::min( top, other.top );
right = std::max( right, other.right );
bottom = std::max( bottom, other.bottom );
}
};
struct edgeRecord
{
int startx; /// The leftmost position for this edge for the given scanline
int endx; /// The rightmost position for the given scanline
enum { leading, trailing } edgeType; /// Whether it is a leading or trailing edge
const ovalRecord *oval;
bool operator<( const struct edgeRecord& other ) const
{
return this->startx < other.startx;
}
void set_span( float x1, float x2 )
{
if( x1 < x2 )
{
startx = (int) std::floor( x1 );
endx = (int) std::ceil( x2 );
}
else
{
startx = (int) std::floor( x2 );
endx = (int) std::ceil( x1 );
}
}
};
struct overlapRecord
{
int index;
floatBounds bounds;
bool operator<( const struct overlapRecord& other ) const
{
bool is_less = true;
if( other.bounds.left <= bounds.left )
{
if( other.bounds.left == bounds.left )
{
if( other.bounds.top <= bounds.top )
{
is_less = false;
}
}
else is_less = false;
}
return is_less;
}
};
/** ---------------------------------------------------------------------------
* \fn computeBounds
* \description This function compute the bounds of a rotated oval.
---------------------------------------------------------------------------- */
static floatBounds computeBounds( const ovalRecord& oval )
{
float sinT = std::sin( oval.angle );
float cosT = std::cos( oval.angle );
float cosrx = cosT * oval.radiusx;
float sinrx = sinT * oval.radiusx;
float cosry = cosT * oval.radiusy;
float sinry = sinT * oval.radiusy;
float dx = std::hypot( cosrx, sinry );
float dy = std::hypot( cosry, sinrx );
return floatBounds{
oval.centerx - dx,
oval.centery - dy,
oval.centerx + dx,
oval.centery + dy
};
}
/** ---------------------------------------------------------------------------
* \fn intervals_intersect
* \description Determines whether an interval defined by a1-a2 overlaps with
* an interval defined by b1-b2. The two intervals are said to overlap if
* the a1 is less than a2 and the range a1-a2 covers any value also covered
* by b1-b2.
---------------------------------------------------------------------------- */
static bool intervals_intersect( float a1, float a2, float b1, float b2 )
{
return ( a1 < a2 ) and ( not ( a2 < b1 or b2 < a1 ) );
}
/** ---------------------------------------------------------------------------
* \fn computeOverlap
* \description Determine whether two bounding boxes overlap, and if so, by
* how much.
---------------------------------------------------------------------------- */
bool computeOverlap( const floatBounds& one, const floatBounds& two, float *area_one, float *area_two )
{
bool overlap = false;
float ww_span = std::min( one.right, two.right ) - std::max( one.left, two.left );
float hh_span = std::min( one.bottom, two.bottom ) - std::max( one.top, two.top );
if( 0.f < ww_span and 0.f < hh_span )
{
float overlap_area = ww_span * hh_span;
*area_one = overlap_area / ( ( one.right - one.left ) * ( one.bottom - one.top ) );
*area_two = overlap_area / ( ( two.right - two.left ) * ( two.bottom - two.top ) );
overlap = true;
}
return overlap;
}
/** ---------------------------------------------------------------------------
* \fn compute_oval_roots
* \description Given a value y, this routine will find the places (if any) where
* the oval intersects.
---------------------------------------------------------------------------- */
static int compute_oval_roots( float xx[2], float yy, const ovalRecord& oval )
{
float sinT = sin( oval.angle );
float cosT = cos( oval.angle );
float sin2T = sinT * sinT;
float cos2T = cosT * cosT;
float rx2 = oval.radiusx * oval.radiusx;
float ry2 = oval.radiusy * oval.radiusy;
float dy = yy - oval.centery;
float aa = rx2 * sin2T + ry2 * cos2T;
float bb = 2.f * dy * sinT * cosT * ( ry2 - rx2 );
float cc = dy * dy * ( rx2 * cos2T + ry2 * sin2T ) - rx2 * ry2;
float radical = bb * bb - 4.f * aa * cc;
int num_roots;
// If the radical is positive, then there are two roots
if( 0.f < radical )
{
num_roots = 2;
float sr = sqrt( radical ); // This is always positive
xx[ 0 ] = oval.centerx + ( ( 0.f - sr - bb ) / ( 2.f * aa ) );
xx[ 1 ] = oval.centerx + ( ( sr - bb ) / ( 2.f * aa ) );
}
else if( 0.f == radical ) // There is only one root
{
num_roots = 1;
xx[ 0 ] = oval.centerx + ( bb / ( -2.f * aa ) );
}
else
{
num_roots = 0;
}
return num_roots;
}
/** ---------------------------------------------------------------------------
* \fn compute_sdf
* \description compute the signed distance to an oval. The distance is positive
* if outside, negative if inside
---------------------------------------------------------------------------- */
static float compute_sdf( const ovalRecord *oval, float xx, float yy )
{
float dx = xx - oval->centerx;
float dy = yy - oval->centery;
float rr;
if( dx != 0.f or dy != 0.f )
{
float angle = oval->angle - atan2( dy, dx );
float sinT = sin( angle );
float cosT = cos( angle );
float a2 = oval->radiusx * oval->radiusx;
float b2 = oval->radiusy * oval->radiusy;
float r2 = ( a2 * b2 ) / ( a2 * sinT * sinT + b2 * cosT * cosT );
rr = hypot( dx, dy ) - sqrt( r2 );
}
else // the point is in the center
{
rr = -std::min( oval->radiusx, oval->radiusy );
}
return rr;
}
/** ---------------------------------------------------------------------------
* \fn aa_case_1
---------------------------------------------------------------------------- */
static float aa_case_1( float p0, float p1, float p2 )
{
// 0--- + p0 --- p2
// | | | |
// +--- + p1 --- p3
assert( p0 <= 0.f );
assert( 0.f <= p1 );
assert( 0.f <= p2 );
float s1 = p0 / ( p0 - p1 );
float s2 = p0 / ( p0 - p2 );
return 0.5f * s1 * s2;
}
/** ---------------------------------------------------------------------------
* \fn aa_case_2
---------------------------------------------------------------------------- */
static float aa_case_2( float p0, float p1, float p2, float p3 )
{
// 0--- + p0 --- p2
// | | | |
// 0--- + p1 --- p3
assert( p0 < 0.f );
assert( p1 < 0.f );
assert( 0.f <= p2 );
assert( 0.f <= p3 );
float s1 = p0 / ( p0 - p2 );
float s2 = p1 / ( p1 - p3 );
return 0.5f * ( s1 + s2 );
}
/** ---------------------------------------------------------------------------
* \fn aa_case_3
---------------------------------------------------------------------------- */
static float aa_case_3( float p0, float p1, float p2, float p3 )
{
// +--- 0 p0 --- p2
// | | | |
// 0--- + p1 --- p3
assert( 0.f <= p0 );
assert( p1 < 0.f );
assert( p2 < 0.f );
assert( 0.f <= p3 );
return aa_case_1( p1, p3, p0 ) + aa_case_1( p2, p0, p3 );
}
/** ---------------------------------------------------------------------------
* \fn aa_case_4
---------------------------------------------------------------------------- */
static float aa_case_4( float p0, float p1, float p2, float p3, float p4 )
{
// 0--- 0 p0 --- p2
// | 0 | | p4 |
// 0--- 0 p1 --- p3
float rr;
assert( 0 <= p0 );
assert( 0 <= p1 );
assert( 0 <= p2 );
assert( 0 <= p3 );
if( p4 < 0.f )
{
float s0 = p4 / ( p4 - p0 );
float s1 = p4 / ( p4 - p1 );
float s2 = p4 / ( p4 - p2 );
float s3 = p4 / ( p4 - p3 );
float r1 = 0.25f * ( s0 + s1 + s2 + s3 );
rr = r1 * r1;
}
else rr = 0.f;
return rr;
}
/** ---------------------------------------------------------------------------
* \fn compute_aa_pixel
* \description Given one or more ovals, compute the contribution. The approach
* here is to compute the signed distance for each oval at each corner and
* then handle each case.
---------------------------------------------------------------------------- */
static float compute_aa_pixel( const std::set< const ovalRecord*>& aalist, float xx, float yy )
{
float farr = hypot( (*aalist.begin())->radiusx, (*aalist.begin())->radiusy );
float p0 = farr;
float p1 = farr;
float p2 = farr;
float p3 = farr;
// p0 --- p2
// | p4 |
// p1 --- p3
for( const auto& one : aalist )
{
p0 = std::min( p0, compute_sdf( one, xx, yy ) );
p1 = std::min( p1, compute_sdf( one, xx, yy + 1.f ) );
p2 = std::min( p2, compute_sdf( one, xx + 1.f, yy ) );
p3 = std::min( p3, compute_sdf( one, xx + 1.f, yy + 1.f ) );
}
int which = 0x0;
if( p0 < 0.f ) which |= 0x01;
if( p1 < 0.f ) which |= 0x02;
if( p2 < 0.f ) which |= 0x04;
if( p3 < 0.f ) which |= 0x08;
// There are 16 possibilities that map to four distinct cases
float rr = 0.f;
if( which == 0x0 or which == 0xF )
{
float p4 = farr; // only if needed
for( const auto& one : aalist )
{
p4 = std::min( p4, compute_sdf( one, xx + 0.5f, yy + 0.5f ) );
}
if( which == 0x0 )
{
rr = aa_case_4( p0, p1, p2, p3, p4 );
}
else
{
rr = 1.f - aa_case_4( -p0, -p1, -p2, -p3, -p4 );
}
}
else
{
switch( which )
{
case 0x1: rr = aa_case_1( p0, p1, p2 ); break;
case 0x2: rr = aa_case_1( p1, p3, p0 ); break;
case 0x3: rr = aa_case_2( p0, p1, p2, p3 ); break;
case 0x4: rr = aa_case_1( p2, p0, p3 ); break;
case 0x5: rr = aa_case_2( p2, p0, p3, p1 ); break;
case 0x6: rr = aa_case_3( p0, p1, p2, p3 ); break;
case 0x7: rr = 1.f - aa_case_1( -p3, -p2, -p1 ); break;
case 0x8: rr = aa_case_1( p3, p2, p1 ); break;
case 0x9: rr = aa_case_3( p1, p3, p0, p2 ); break;
case 0xA: rr = aa_case_2( p1, p3, p0, p2 ); break;
case 0xB: rr = 1.f - aa_case_1( -p2, -p0, -p3 ); break;
case 0xC: rr = aa_case_2( p3, p2, p1, p0 ); break;
case 0xD: rr = 1.f - aa_case_1( -p1, -p3, -p0 ); break;
case 0xE: rr = 1.f - aa_case_1( -p0, -p1, -p2 ); break;
}
}
return rr;
}
/** ---------------------------------------------------------------------------
* \fn computeEdgeList
* \description For a given scan line value (scanY) find all intersecting ovals
* and create an edgelist that can be scanned.
* \param scanY The vertical position of the scanline for which to return
* the edge list.
* \param ol The list of oval that are being rasterized
* \param blist The list of bounding boxes for the corresponding list of ovals
* \param bounds The union of all the bounds for all the ovals in the list
* \param edgeList A place to return the edges that intersect the given Y coordinate
* \returns An integer that specifies the next scanline that will contain
* an edge.
---------------------------------------------------------------------------- */
static int computeEdgeList( int scanY,
const std::vector<ovalRecord>& ol,
const std::vector<floatBounds>& blist,
const floatBounds& bounds,
std::vector<edgeRecord> *edgeList )
{
float topY = scanY;
float bottomY = topY + 1.f;
float nextBottomY = bottomY + 1.f;
float nextY = bounds.bottom;
for( int ii = 0; ii < blist.size(); ii += 1 )
{
if( intervals_intersect( blist[ ii ].top, blist[ ii ].bottom, topY, bottomY ) )
{
float topx[ 2 ];
float botx[ 2 ];
int num_top = compute_oval_roots( topx, topY, ol[ ii ] );
int num_bottom = compute_oval_roots( botx, bottomY, ol[ ii ] );
if( num_top == 2 and num_bottom == 2 ) // the most common case
{
edgeRecord er1, er2;
er1.set_span( topx[ 0 ], botx[ 0 ] );
er2.set_span( topx[ 1 ], botx[ 1 ] );
er1.edgeType = edgeRecord::leading;
er2.edgeType = edgeRecord::trailing;
er1.oval = & ol[ ii ];
er2.oval = & ol[ ii ];
edgeList->push_back( er1 );
edgeList->push_back( er2 );
}
else if( num_top == 2 ) // num_bottom is either zero or one
{
float lowx;
if( num_bottom == 1 )
lowx = botx[ 0 ];
else
lowx = 0.5f * ( topx[ 0 ] + topx[ 1 ] );
edgeList->push_back( {
(int) std::floor( topx[ 0 ] ),
(int) std::ceil( lowx ),
edgeRecord::leading,
& ol[ ii ]
});
edgeList->push_back( {
(int) std::floor( lowx ),
(int) std::ceil( topx[ 1 ] ),
edgeRecord::trailing,
& ol[ ii ]
});
}
else if( num_bottom == 2 ) // then num_top is either zero or one
{
float hix;
if( num_top == 1 )
hix = topx[ 0 ];
else
hix = 0.5f * ( botx[ 0 ] + botx[ 1 ] );
edgeList->push_back( {
(int) std::floor( botx[ 0 ] ),
(int) std::ceil( hix ),
edgeRecord::leading,
& ol[ ii ]
});
edgeList->push_back( {
(int) std::floor( hix ),
(int) std::ceil( botx[ 1 ] ),
edgeRecord::trailing,
& ol[ ii ]
});
}
else // The remaining cases are all pathological - we use the bounds
{
if( topY < blist[ ii ].bottom and blist[ ii ].top < bottomY )
{
float midx;
if( num_top == 1 )
midx = topx[ 0 ];
else
midx = 0.5f * (blist[ ii ].left + blist[ ii ].right);
edgeList->push_back( {
(int) std::floor( blist[ ii ].left ),
(int) std::ceil( midx ),
edgeRecord::leading,
&ol[ ii ]
} );
if( num_bottom == 1 )
midx = botx[ 0 ];
else
midx = 0.5f * (blist[ ii ].left + blist[ ii ].right);
edgeList->push_back( {
(int) std::floor( midx ),
(int) std::ceil( blist[ ii ].right ),
edgeRecord::trailing,
&ol[ ii ]
} );
}
else
{
nextY = bottomY;
}
}
}
else // this interval does not intersect the current line
{
if( topY <= blist[ ii ].top and blist[ ii ].top < nextY )
{
nextY = blist[ ii ].top;
}
}
}
int next_scanY;
if( not edgeList->empty() )
{
next_scanY = scanY + 1;
}
else // the edgelist is empty, nothing intersected our span
{
next_scanY = std::max( (int) std::floor( nextY ), scanY + 1 );;
}
return next_scanY;
}
/** ---------------------------------------------------------------------------
* \fn extend_or_push
---------------------------------------------------------------------------- */
static void push_or_merge_run( std::vector< pixelRun >& rr, const pixelRun& pr )
{
if( 0.f < pr.value )
{
if( rr.empty() or
rr.back().value != pr.value or
rr.back().lineY != pr.lineY or
rr.back().endX != pr.startX )
{
rr.push_back( pr );
}
else
{
rr.back().endX = pr.endX;
}
}
}
/** ---------------------------------------------------------------------------
* \fn ovalListToRaster
---------------------------------------------------------------------------- */
std::vector<pixelRun> ovalListToRaster( const std::vector<ovalRecord>& ol, int width, int height )
{
std::vector<pixelRun> rr;
if( not ol.empty() )
{
std::vector< floatBounds > blist;
floatBounds bounds = computeBounds( ol[ 0 ] );
blist.push_back( bounds );
for( int ii = 1; ii < ol.size(); ii += 1 )
{
floatBounds one = computeBounds( ol[ ii ] );
bounds.add( one );
blist.push_back( one );
}
int topY = (int)std::max( 0.f, bounds.top );
int endY = (int)std::min( (float)height, std::ceil( bounds.bottom ) );
int right_edge = (int)std::min((float) width, std::ceil( bounds.right ) );
int scanY = topY;
pixelRun pr;
std::vector<edgeRecord> edgeList;
if( scanY < endY )
{
for(;;)
{
pr.lineY = scanY;
// For the given scanline find all the edges that are relevant
int nextY = computeEdgeList( scanY, ol, blist, bounds, &edgeList );
if( not edgeList.empty() )
{
std::sort( edgeList.begin(), edgeList.end() );
std::set< const ovalRecord *> aalist; // for anti-aliased pixels
std::set< const ovalRecord *> xxlist; // to track inside/outside
pr.startX = std::max( 0, edgeList[ 0 ].startx );
if( pr.startX < right_edge )
{
do
{
pr.endX = right_edge; // assume that we're going to the edge
// For each value of x, we need to go through the list of edges
// and collect the oval edges that would need to be evaluated there
for( const auto& edge : edgeList )
{
if( edge.startx <= pr.startX ) // the edge is to left or at us
{
if( edge.edgeType == edgeRecord::leading )
{
if( pr.startX < edge.endx ) // we're inside the edge
{
aalist.insert( edge.oval );
}
else // we're completely to the right of this edge
{
xxlist.insert( edge.oval );
}
}
else // edge.Type == edgeRecord::trailing
{
xxlist.erase( edge.oval ); // this ends the solid run
if( pr.startX < edge.endx ) // we're in the active section
{
aalist.insert( edge.oval );
}
}
}
else // this edge starts is beyond our current scan point - done with this run
{
// signal for the next run to begin at the start of the next edge
pr.endX = std::min( edge.startx, right_edge );
break;
}
}
if( aalist.empty() )
{
if( not xxlist.empty() )
{
pr.value = 1.f; // a solid run
push_or_merge_run( rr, pr );
}
}
else // we might need to anti-alias an edge
{
pr.endX = pr.startX + 1; // when we have active edges, go one pixel at the time
if( xxlist.empty() )
{
pr.value = compute_aa_pixel( aalist, pr.startX, pr.lineY );
}
else // we're a partial edge that is completely inside of another oval
{
pr.value = 1.f;
}
push_or_merge_run( rr, pr );
aalist.clear();
}
xxlist.clear();
pr.startX = pr.endX;
} while( pr.startX < right_edge );
}
}
if( nextY < endY )
{
scanY = nextY;
edgeList.resize( 0 );
}
else break;
}
}
}
return rr;
}
/** ---------------------------------------------------------------------------
* \fn deduplicateOvalList
---------------------------------------------------------------------------- */
int deduplicateOvalList( std::vector< ovalRecord >& ovalList, float cover_limit )
{
int num_removed = 0;
if( 1 < ovalList.size() and 0.f < cover_limit )
{
std::vector< overlapRecord > xlist;
xlist.reserve( ovalList.size() );
int ii = 0;
for(; ii < ovalList.size(); ii += 1 )
{
xlist.push_back( { ii, computeBounds( ovalList[ ii ] ) } );
}
std::sort( xlist.begin(), xlist.end() );
std::set< int > skips;
for( int jj = 0; jj < xlist.size(); jj += 1 )
{
if( skips.count( jj ) == 0 ) // if we haven't deleted this one
{
for( ii = jj + 1; ii < xlist.size(); ii += 1 )
{
if( skips.count( ii ) == 0 ) // we haven't deleted this one
{
if( xlist[ ii ].bounds.left < xlist[ jj ].bounds.right )
{
float cover_jj, cover_ii;
if( computeOverlap( xlist[ jj ].bounds, xlist[ ii ].bounds,
& cover_jj, & cover_ii ) )
{
if( cover_jj <= cover_ii and cover_limit <= cover_ii )
{
skips.insert( ii );
}
else if( cover_ii < cover_jj and cover_limit <= cover_jj )
{
skips.insert( jj );
break; // we removed the pivot, so skip to the next
}
}
}
else break; // the remaining rectangles are to the right
}
}
}
}
if( not skips.empty() )
{
std::vector< ovalRecord > updatedList;
for( ii = 0; ii < ovalList.size(); ii += 1 )
{
if( skips.count( ii ) == 0 ) // don't skip this one
{
updatedList.push_back( ovalList[ xlist[ ii ].index ] );
}
}
ovalList.swap( updatedList );
num_removed = skips.size();
}
}
return num_removed;
}
/** ---------------------------------------------------------------------------
* ---------------------------TEST CASES --------------------------------------
---------------------------------------------------------------------------- */
#ifdef TESTING
TEST_SUITE_BEGIN( "OvalRasterizer_UnitTests");
TEST_CASE( "AddBounds" )
{
floatBounds r1{ 10.f, 20.f, 30.f, 40.f };
floatBounds r2{ 0.f, 10.f, 40.f, 50.f };
r1.add( r2 );
CHECK( r1.left == 0.f );
CHECK( r1.top == 10.f );
CHECK( r1.right == 40.f );
CHECK( r1.bottom == 50.f );
}
TEST_CASE( "ComputeBounds0" )
{
floatBounds rr = computeBounds( {
.centerx = 100.f,
.centery = 200.f,
.radiusx = 10.f,
.radiusy = 30.f,
.angle = 0.f
} );
CHECK( rr.left == doctest::Approx( 100.f - 10.f ) );
CHECK( rr.right == doctest::Approx( 100.F + 10.f ) );
CHECK( rr.top == doctest::Approx( 200.f - 30.f ) );
CHECK( rr.bottom == doctest::Approx( 200.f + 30.f ) );
}
TEST_CASE( "ComputeBounds90" )
{
floatBounds rr = computeBounds( {
.centerx = 100.f,
.centery = 200.f,
.radiusx = 10.f,
.radiusy = 30.f,
.angle = M_PI_2
} );
CHECK( rr.left == doctest::Approx( 100.f - 30.f ) );
CHECK( rr.right == doctest::Approx( 100.F + 30.f ) );
CHECK( rr.top == doctest::Approx( 200.f - 10.f ) );
CHECK( rr.bottom == doctest::Approx( 200.f + 10.f ) );
}
TEST_CASE( "Intervals Intersect" )
{
CHECK( intervals_intersect( 10.f, 20.f, 30.f, 31.f ) == false ); // to the left
CHECK( intervals_intersect( 40.f, 50.f, 30.f, 31.f ) == false ); // to the right
CHECK( intervals_intersect( 40.f, 40.f, 30.f, 31.f ) == false ); // null interval
CHECK( intervals_intersect( 40.f, 39.f, 30.f, 31.f ) == false ); // null interval too
CHECK( intervals_intersect( 10.f, 30.5f, 30.f, 31.f ) ); // left overlap
CHECK( intervals_intersect( 30.5f, 40.f, 30.f, 31.f ) ); // right overlap
CHECK( intervals_intersect( 10.f, 40.f, 30.f, 31.f ) ); // complete overlap
CHECK( intervals_intersect( 30.1f, 30.9f, 30.f, 31.f ) ); // completely contained
CHECK( intervals_intersect( 10.f, 20.f, 0.f, 10.f ) ); // touching on the left
CHECK( intervals_intersect( 10.f, 20.f, 20.f, 30.f) ); // touching on the right
}
TEST_CASE( "Compute Roots" )
{
ovalRecord oval = {
.centerx = 10.f,
.centery = 5.f,
.radiusx = 3.f,
.radiusy = 4.f,
.angle = M_PI_4
};
float xx[ 2 ];
int num_roots = compute_oval_roots( xx, 6.f, oval ); // above the center
CHECK( num_roots == 2 );
CHECK( xx[ 0 ] == doctest::Approx( 6.464482f ) );
CHECK( xx[ 1 ] == doctest::Approx( 12.975518f ) );
float dx_above = xx[ 1 ] - xx[ 0 ];
num_roots = compute_oval_roots( xx, 4.f, oval ); // below the center
CHECK( num_roots == 2 );
CHECK( xx[ 0 ] < xx[ 1 ] );
CHECK( xx[ 0 ] == doctest::Approx( 7.024482f ) );
CHECK( xx[ 1 ] == doctest::Approx( 13.535518f ) );
float dx_below = xx[ 1 ] - xx[ 0 ];
// Since we test one line line above and one line below the center of the
// oval, we expect the distance between the roots to be the same
CHECK( ( dx_above - dx_below ) == doctest::Approx( 0.f ) );
oval.angle = 0.f; // rest the angle to check for one root
num_roots = compute_oval_roots( xx, 1., oval );
CHECK( num_roots == 1 );
CHECK( xx[ 0 ] < xx[ 1 ] );
CHECK( xx[ 0 ] == doctest::Approx( 10.f ) );
// Test above and below the oval to confirm that no roots can be found there
num_roots = compute_oval_roots( xx, 0.f, oval ); // below
CHECK( num_roots == 0 );
num_roots = compute_oval_roots( xx, 10.f, oval ); // above
CHECK( num_roots == 0 );
}
TEST_CASE("edgeRecord_sort")
{
std::vector< edgeRecord > edgeList;
edgeRecord one{ .startx = 10, .endx = 11, .edgeType = edgeRecord::leading, .oval = nullptr };
edgeRecord two{ .startx = 20, .endx = 21, .edgeType = edgeRecord::leading, .oval = nullptr };
edgeRecord three{ .startx = 30, .endx = 31, .edgeType = edgeRecord::trailing, .oval = nullptr };
CHECK( one < two );
CHECK( two < three );
CHECK( one < three );
edgeList.push_back( three );
edgeList.push_back( two );
edgeList.push_back( one );
std::sort( edgeList.begin(), edgeList.end() );
CHECK( edgeList[ 0 ] < edgeList[ 1 ] );
CHECK( edgeList[ 1 ] < edgeList[ 2 ] );
}
TEST_CASE("edgeRecord_set_span")
{
edgeRecord er;
er.set_span( 1.5, 2.5 );
CHECK( er.startx == 1 );
CHECK( er.endx == 3 );
er.set_span( 2.5, 1.5 );
CHECK( er.startx == 1 );
CHECK( er.endx == 3 );
}
TEST_CASE("compute_sdf")
{
ovalRecord oval{ 10.f, 20.f, 3.f, 4.f, M_PI_2 };
CHECK( compute_sdf( & oval, 10.f, 20.f ) == -3.f );
CHECK( compute_sdf( & oval, 10.f, 0.f ) == doctest::Approx( 17.f ) );
CHECK( compute_sdf( & oval, 0.f, 20.f ) == doctest::Approx( 6.f ) );
CHECK( compute_sdf( & oval, 8.f, 20.f ) == doctest::Approx( -2.f ) );
}
TEST_CASE("AA_Case_Tests")
{
CHECK( aa_case_1( -1.f, 0.f, 0.f ) == doctest::Approx( .5f ) );
CHECK( aa_case_1( -1.f, 1.f, 1.f ) == doctest::Approx( 0.125f ) );
CHECK( aa_case_2( -1.f, -1.f, 0.f, 0.f ) == doctest::Approx( 1.f ) );
CHECK( aa_case_2( -1.f, -1.f, 1.f, 1.f ) == doctest::Approx( 0.5f ) );
CHECK( aa_case_3( 0.f, -1.f, -1.f, 0.f ) == doctest::Approx( 1.f ) );
CHECK( aa_case_3( 1.f, -1.f, -1.f, 1.f ) == doctest::Approx( 0.25f ) );
CHECK( aa_case_4( 1.f, 1.f, 1.f, 1.f, 0.f ) == doctest::Approx( 0.f ) );
CHECK( aa_case_4( 1.f, 1.f, 1.f, 1.f, -1.f ) == doctest::Approx( 0.25f ) );
CHECK( aa_case_4( 0.f, 0.f, 0.f, 0.f, -1.f ) == doctest::Approx( 1.0f ) );
}
TEST_CASE( "Merge and Push Runs")
{
std::vector<pixelRun> runList;
push_or_merge_run( runList, {101, 100, 200, 1.f} );
CHECK( runList.size() == 1 ); // check if empty
push_or_merge_run( runList, {101, 200, 210, .9f} );
CHECK( runList.size() == 2 ); // non-match on the value
push_or_merge_run( runList, {102, 210, 220, .9f} );
CHECK( runList.size() == 3 ); // non-match on the lineY
push_or_merge_run( runList, {102, 220, 230, .9f} );
CHECK( runList.size() == 3 );
CHECK( runList.back().endX == 230 );
}
TEST_CASE( "CompareOverlapRecords")
{
overlapRecord one { 1, { 10.f, 20.f, 50.f, 60.f } };
overlapRecord two { 2, { 15.f, 25.f, 55.f, 65.f } };
overlapRecord three{ 3, { 10.f, 25.f, 50.f, 60.f } };
overlapRecord four{ 4, { 10.f, 20.f, 45.f, 65.f } };
CHECK( one < two ); // trivial case
CHECK( not ( two < one ) ); // reverse
CHECK( one < three ); // left edge is aligned
CHECK( not ( three < one ) ); // reverse
CHECK( not ( one < four ) ); // left and top match, not strictly less
CHECK( not ( four < one ) );
}
TEST_CASE( "ComputeOverlap")
{
floatBounds one{ 10.f, 10.f, 20.f, 20.f };
floatBounds two{ 15.f, 15.f, 25.f, 25.f };
floatBounds three{ 30.f, 10.f, 40.f, 20.f }; // to the right
floatBounds four{ 10.f, 30.f, 20.f, 40.f }; // below
floatBounds five{ 10.f, 15.f, 20.f, 20.f }; // contained
float area_one, area_two;
REQUIRE( computeOverlap( one, two, & area_one, & area_two ) );
CHECK( area_one == doctest::Approx( 0.25f ) );
CHECK( area_two == doctest::Approx( 0.25f ) );
CHECK( computeOverlap( one, three, & area_one, & area_two ) == false );
CHECK( computeOverlap( one, four, & area_one, & area_two ) == false );
REQUIRE( computeOverlap( one, five, & area_one, & area_two ) );
CHECK( area_one == doctest::Approx( 0.5f ) );
CHECK( area_two == doctest::Approx( 1.f ) );
}
TEST_CASE("Compute Edge List Case 2-{2,1}" )
{
std::vector< ovalRecord > ovalList;
ovalList.push_back( { 16.5f, 11.5f, 1.0f, 1.5f, 0.f } );
floatBounds bounds = computeBounds( ovalList[ 0 ] );
std::vector< floatBounds > blist;
blist.push_back( bounds );
// CASE 1-2
std::vector< edgeRecord > edgeList;
int nextY = computeEdgeList( 10, ovalList, blist, bounds, & edgeList );