Article ID: 243285 - Last Review: February 12, 2007 - Revision: 1.5

This article was previously published under Q243285

The Win32 API **GetGlyphOutline** function can return native glyph outline data from a TrueType font. To draw a TrueType glyph outline, the data must be converted from its native B-Spline definition to a sequence of Bezier line definitions. Then the **PolyBezier** Win32 API function can be used to draw the outline.

The **GetGlyphOutline** function in the Win32 Application Programming Interface(API) can retrieve a TrueType outline. The GGO_NATIVE format option fills a buffer with Quadratic B-Spline curves for a TrueType outline. Quadratic B-Splines are used by TrueType to describe the glyph outline in a TrueType font file. To draw these outline curves one can implement a B-Spline drawing function or use the **PolyBezier** function from the Win32 API.

Quadratic B-Spline curves are a class of parametric curves that define the path of multiple curve segments via a few control points. A Quadratic curve is a second order parametric curve. There is no function in the API to draw a Quadratic Spline directly but if the Quadratic is converted to a Cubic it can be drawn with the Win32 API function for drawing a Bezier curve; called**PolyBezier**.

Quadratic B-Spline curves in particular and parametric curves in general are a well-researched topic of graphics in computer science. They can also be quite complex. Algorithms have been published in various texts that can be used to implement a function to draw a Quadratic Spline, but describing such an algorithm is beyond the scope of this article.

The**PolyBezier** function can draw a Quadratic Spline because a Bezier curve is a cubic or third order parametric curve. Since a Quadratic Spline is a second order equation, it can be expressed in terms of the higher order cubic equation. Although an equation for expressing a quadratic as a cubic is given in the sample code, its derivation is not discussed in this article.

The sample code in this article is a demonstration of how to parse a GGO_NATIVE glyph buffer returned by the**GetGlyphOutline** function. The buffer returned by the GGO_NATIVE format flag conforms to the **TTPOLYGONHEADER** structure. The **TTPOLYGONHEADER** structure and the data that immediately follows it constitute one contour of a TrueType glyph. A contour is one complete path of curves that is implicitly closed if it is not explicitly returned that way.

Please see the Platform SDK for documentation on the**TTPOLYGONHEADER** and **TTPOLYCURVE** structures.

A glyph contour consists of multiple curve segments represented by**TTPOLYCURVE** structures. In a contour, the **TTPOLYGONHEADER** is followed by one or more **TTPOLYCURVE** structures and coordinate point data. The **pfxStart** member gives the starting coordinate point of the contour. The count of curve records that follow the **TTPOLYGONHEADER** is given by the **cb** member. The starting point is relative to the origin of the glyph. The origin of a glyph is the lower left corner of the character at the character's baseline.

Each**TTPOLYCURVE** curve record (a curve segment) consists of either Quadratic B-Spline control points or simple Polyline points. The count of points is given by the **TTPOLYCURVE****cpfx** member. The curve type of either spline or polyline is given by the **wType** member. The array of coordinate points immediately follow the structure. The starting point of the curve is given by the **apfx** member.

Since a glyph may contain more than one contour, the buffer contains one or more groups of**TTPOLYGONHEADER** structures and data. Subsequent contours are packed immediately following the previous one in the native buffer. The next contour starts with a **TTPOLYGONHEADER** at the next byte beyond the last point of the previous curve record.

This sample code draws the outline of a TrueType glyph by parsing the GGO_NATIVE buffer to create a list of Bezier line segments that form each contour. The list of Bezier line segments is then drawn using**PolyBezier**. The code that parses the buffer is in the **DrawT2Outline** function.

The first step to create a list of Bezier lines is to determine the size of the buffer for the list. Four points define Bezier lines. The**PolyBezier** function interprets an array of points as being one continuous line of Bezier segments where the start of the next line is coincident with the endpoint of the previous line. Thus, only three points are needed to describe an additional Bezier line segment.

The GGO_NATIVE buffer may contain either a polyline curve or a Quadratic B-Spline curve. Two points define a line segment while three points define a B-Spline. Since each type is to be drawn with a Bezier line using PolyBezier, the worst case scenario occurs when one contour that is entirely composed of line segments expands to multiple Beziers.

Note that to express an additional curve segment in a B-Spline curve representation requires only one additional point. That point explicitly defines the "B" or off curve point and implicitly defines the additional on curve point. The on curve point is the midpoint to the next "B" point. Thus either an additional line segment or an additional curve segment will expand to three additional points of a Bezier line.

The code assumes that the entire native buffer will consist of**POINTFX** structures so it can determine the largest possible number of points represented by the buffer. The actual number is slightly smaller since there is structure overhead in describing the contours and curves. The size of the buffer for the Bezier list is given by the maximum possible number of points multiplied by the data size of a **POINT** structure and multiplied by three. Three is the number of additional points that are needed for each additional line segment or quadratic spline segment when converted to a Bezier.

Once the Bezier buffer has been allocated the code parses the native buffer by starting at the first**TTPOLYGONHEADER**. During an iteration of the loop the code processes one contour and draws it. A Second inner loop parses each curve type.

In the case of a polyline curve (TT_PRIM_LINE), each line segment of the polyline is converted and appended to the list of Beziers with the**AppendPolyLineToBezier** function. If the curve is a Quadratic B-Spline (TT_PRIM_QSPLINE), the **AppendQuadBSplineToBezier** function converts and appends the Quadratic B-Spline. Each of these functions uses a loop to parse out each segment of the curve into its independent control points. Then the line or spline is converted to a Bezier and appended to the list of Beziers.

A Bezier line can draw a straight line easily. The start and ending vectors simply point at the opposite end of the line segment. This is done in the**MakeBezierFromLine** function.

To convert a quadratic spline into a cubic Bezier spline requires expressing the cubic's control points in terms of the quadratic's control points. The equation to translate the control points is located in the**MakeBezierFromQBSpline** function.

Before drawing the contour, the code ensures that the path is closed by calling the**CloseContour** function. The function is called only if the start and end points of the sequence of Beziers are not coincident. Then the **PolyBezier** function is called.

After the contour is drawn, the next contour's**TTPOLYGONHEADER** is found by advancing the lpHeader pointer beyond the end of the records in the current contour. If this results in a pointer value beyond the end of the native buffer, the code has processed all of the contours and exits.

Quadratic B-Spline curves are a class of parametric curves that define the path of multiple curve segments via a few control points. A Quadratic curve is a second order parametric curve. There is no function in the API to draw a Quadratic Spline directly but if the Quadratic is converted to a Cubic it can be drawn with the Win32 API function for drawing a Bezier curve; called

Quadratic B-Spline curves in particular and parametric curves in general are a well-researched topic of graphics in computer science. They can also be quite complex. Algorithms have been published in various texts that can be used to implement a function to draw a Quadratic Spline, but describing such an algorithm is beyond the scope of this article.

The

The sample code in this article is a demonstration of how to parse a GGO_NATIVE glyph buffer returned by the

Please see the Platform SDK for documentation on the

A glyph contour consists of multiple curve segments represented by

Each

Since a glyph may contain more than one contour, the buffer contains one or more groups of

This sample code draws the outline of a TrueType glyph by parsing the GGO_NATIVE buffer to create a list of Bezier line segments that form each contour. The list of Bezier line segments is then drawn using

The first step to create a list of Bezier lines is to determine the size of the buffer for the list. Four points define Bezier lines. The

The GGO_NATIVE buffer may contain either a polyline curve or a Quadratic B-Spline curve. Two points define a line segment while three points define a B-Spline. Since each type is to be drawn with a Bezier line using PolyBezier, the worst case scenario occurs when one contour that is entirely composed of line segments expands to multiple Beziers.

Note that to express an additional curve segment in a B-Spline curve representation requires only one additional point. That point explicitly defines the "B" or off curve point and implicitly defines the additional on curve point. The on curve point is the midpoint to the next "B" point. Thus either an additional line segment or an additional curve segment will expand to three additional points of a Bezier line.

The code assumes that the entire native buffer will consist of

Once the Bezier buffer has been allocated the code parses the native buffer by starting at the first

In the case of a polyline curve (TT_PRIM_LINE), each line segment of the polyline is converted and appended to the list of Beziers with the

A Bezier line can draw a straight line easily. The start and ending vectors simply point at the opposite end of the line segment. This is done in the

To convert a quadratic spline into a cubic Bezier spline requires expressing the cubic's control points in terms of the quadratic's control points. The equation to translate the control points is located in the

Before drawing the contour, the code ensures that the path is closed by calling the

After the contour is drawn, the next contour's

/****************************************************************************
* FUNCTION : IntFromFixed
* RETURNS : int value approximating the FIXED value.
****************************************************************************/
int PASCAL NEAR IntFromFixed(FIXED f)
{
if (f.fract >= 0x8000)
return(f.value + 1);
else
return(f.value);
}
/****************************************************************************
* FUNCTION : fxDiv2
* RETURNS : (val1 + val2)/2 for FIXED values
****************************************************************************/
FIXED PASCAL NEAR fxDiv2(FIXED fxVal1, FIXED fxVal2)
{
long l;
l = (*((long far *)&(fxVal1)) + *((long far *)&(fxVal2)))/2;
return(*(FIXED *)&l);
}
/****************************************************************************
* FUNCTION : MakeBezierFromLine
*
* PURPOSE : Converts a line define by two points to a four point Bezier
* spline representation of the line in pPts.
*
*
* RETURNS : number of Bezier points placed into the pPts POINT array.
****************************************************************************/
UINT MakeBezierFromLine( POINT *pPts, POINT startpt, POINT endpt )
{
UINT cTotal = 0;
// starting point of Bezier
pPts[cTotal] = startpt;
cTotal++;
// 1rst Control, pt == endpoint makes Bezier a line
pPts[cTotal].x = endpt.x;
pPts[cTotal].y = endpt.y;
cTotal++;
// 2nd Control, pt == startpoint makes Bezier a line
pPts[cTotal].x = startpt.x;
pPts[cTotal].y = startpt.y;
cTotal++;
// ending point of Bezier
pPts[cTotal] = endpt;
cTotal++;
return cTotal;
}
/****************************************************************************
* FUNCTION : MakeBezierFromQBSpline
*
* PURPOSE : Converts a quadratic spline in pSline to a four point Bezier
* spline in pPts.
*
*
* RETURNS : number of Bezier points placed into the pPts POINT array.
****************************************************************************/
UINT MakeBezierFromQBSpline( POINT *pPts, POINTFX *pSpline )
{
POINT P0, // Quadratic on curve start point
P1, // Quadratic control point
P2; // Quadratic on curve end point
UINT cTotal = 0;
// Convert the Quadratic points to integer
P0.x = IntFromFixed( pSpline[0].x );
P0.y = IntFromFixed( pSpline[0].y );
P1.x = IntFromFixed( pSpline[1].x );
P1.y = IntFromFixed( pSpline[1].y );
P2.x = IntFromFixed( pSpline[2].x );
P2.y = IntFromFixed( pSpline[2].y );
// conversion of a quadratic to a cubic
// Cubic P0 is the on curve start point
pPts[cTotal] = P0;
cTotal++;
// Cubic P1 in terms of Quadratic P0 and P1
pPts[cTotal].x = P0.x + 2*(P1.x - P0.x)/3;
pPts[cTotal].y = P0.y + 2*(P1.y - P0.y)/3;
cTotal++;
// Cubic P2 in terms of Qudartic P1 and P2
pPts[cTotal].x = P1.x + 1*(P2.x - P1.x)/3;
pPts[cTotal].y = P1.y + 1*(P2.y - P1.y)/3;
cTotal++;
// Cubic P3 is the on curve end point
pPts[cTotal] = P2;
cTotal++;
return cTotal;
}
/****************************************************************************
* FUNCTION : AppendPolyLineToBezier
*
* PURPOSE : Converts line segments into their Bezier point
* representation and appends them to a list of Bezier points.
*
* WARNING - The array must have at least one valid
* start point prior to the address of the element passed.
*
* RETURNS : number of Bezier points added to the POINT array.
****************************************************************************/
UINT AppendPolyLineToBezier( LPPOINT pt, POINTFX start, LPTTPOLYCURVE lpCurve )
{
int i;
UINT cTotal = 0;
POINT endpt;
POINT startpt;
POINT bezier[4];
endpt.x = IntFromFixed(start.x);
endpt.y = IntFromFixed(start.y);
for (i = 0; i < lpCurve->cpfx; i++)
{
// define the line segment
startpt = endpt;
endpt.x = IntFromFixed(lpCurve->apfx[i].x);
endpt.y = IntFromFixed(lpCurve->apfx[i].y);
// convert a line to a bezier representation
MakeBezierFromLine( bezier, startpt, endpt );
// append the Bezier to the existing ones
// Point 0 is Point 3 of previous.
pt[cTotal++] = bezier[1]; // Point 1
pt[cTotal++] = bezier[2]; // Point 2
pt[cTotal++] = bezier[3]; // Point 3
}
return cTotal;
}
/****************************************************************************
* FUNCTION : AppendQuadBSplineToBezier
*
* PURPOSE : Converts Quadratic spline segments into their Bezier point
* representation and appends them to a list of Bezier points.
*
* WARNING - The array must have at least one valid
* start point prior to the address of the element passed.
*
* RETURNS : number of Bezier points added to the POINT array.
****************************************************************************/
UINT AppendQuadBSplineToBezier( LPPOINT pt, POINTFX start, LPTTPOLYCURVE lpCurve )
{
WORD i;
UINT cTotal = 0;
POINTFX spline[3]; // a Quadratic is defined by 3 points
POINT bezier[4]; // a Cubic by 4
// The initial A point is on the curve.
spline[0] = start;
for (i = 0; i < lpCurve->cpfx;)
{
// The B point.
spline[1] = lpCurve->apfx[i++];
// Calculate the C point.
if (i == (lpCurve->cpfx - 1))
{
// The last C point is described explicitly
// i.e. it is on the curve.
spline[2] = lpCurve->apfx[i++];
}
else
{
// C is midpoint between B and next B point
// because that is the on curve point of
// a Quadratic B-Spline.
spline[2].x = fxDiv2(
lpCurve->apfx[i-1].x,
lpCurve->apfx[i].x
);
spline[2].y = fxDiv2(
lpCurve->apfx[i-1].y,
lpCurve->apfx[i].y
);
}
// convert the Q Spline to a Bezier
MakeBezierFromQBSpline( bezier, spline );
// append the Bezier to the existing ones
// Point 0 is Point 3 of previous.
pt[cTotal++] = bezier[1]; // Point 1
pt[cTotal++] = bezier[2]; // Point 2
pt[cTotal++] = bezier[3]; // Point 3
// New A point for next slice of spline is the
// on curve C point of this B-Spline
spline[0] = spline[2];
}
return cTotal;
}
/****************************************************************************
* FUNCTION : CloseContour
*
* PURPOSE : Adds a bezier line to close the circuit defined in pt.
*
*
* RETURNS : number of points aded to the pt POINT array.
****************************************************************************/
UINT CloseContour( LPPOINT pt, UINT cTotal )
{
POINT endpt,
startpt; // definition of a line
POINT bezier[4];
// connect the first and last points by a line segment
startpt = pt[cTotal-1];
endpt = pt[0];
// convert a line to a bezier representation
MakeBezierFromLine( bezier, startpt, endpt );
// append the Bezier to the existing ones
// Point 0 is Point 3 of previous.
pt[cTotal++] = bezier[1]; // Point 1
pt[cTotal++] = bezier[2]; // Point 2
pt[cTotal++] = bezier[3]; // Point 3
return 3;
}
/****************************************************************************
* FUNCTION : DrawT2Outline
*
* PURPOSE : Decode the GGO_NATIVE outline, create a sequence of Beziers
* for each contour, draw with PolyBezier. Color and relative
* positioning provided by caller. The coordinates of hDC are
* assumed to have MM_TEXT orientation.
*
* The outline data is not scaled. To draw a glyph unhinted
* the caller should create the font at its EMSquare size
* and retrieve the outline data. Then setup a mapping mode
* prior to calling this function.
*
* RETURNS : none.
****************************************************************************/
void DrawT2Outline(HDC hDC, LPTTPOLYGONHEADER lpHeader, DWORD size)
{
WORD i;
UINT cTotal = 0; // Total points in a contour.
LPTTPOLYGONHEADER lpStart; // the start of the buffer
LPTTPOLYCURVE lpCurve; // the current curve of a contour
LPPOINT pt; // the bezier buffer
POINTFX ptStart; // The starting point of a curve
DWORD dwMaxPts = size/size of(POINTFX); // max possible pts.
DWORD dwBuffSize;
dwBuffSize = dwMaxPts * // Maximum possible # of contour points.
sizeof(POINT) * // sizeof buffer element
3; // Worst case multiplier of one additional point
// of line expanding to three points of a bezier
lpStart = lpHeader;
pt = (LPPOINT)malloc( dwBuffSize );
// Loop until we have processed the entire buffer of contours.
// The buffer may contain one or more contours that begin with
// a TTPOLYGONHEADER. We have them all when we the end of the buffer.
while ((DWORD)lpHeader < (DWORD)(((LPSTR)lpStart) + size) && pt != NULL)
{
if (lpHeader->dwType == TT_POLYGON_TYPE)
// Draw each coutour, currently this is the only valid
// type of contour.
{
// Convert the starting point. It is an on curve point.
// All other points are continuous from the "last"
// point of the contour. Thus the start point the next
// bezier is always pt[cTotal-1] - the last point of the
// previous bezier. See PolyBezier.
cTotal = 1;
pt[0].x = IntFromFixed(lpHeader->pfxStart.x);
pt[0].y = IntFromFixed(lpHeader->pfxStart.y);
// Get to first curve of contour -
// it starts at the next byte beyond header
lpCurve = (LPTTPOLYCURVE) (lpHeader + 1);
// Walk this contour and process each curve( or line ) segment
// and add it to the Beziers
while ((DWORD)lpCurve < (DWORD)(((LPSTR)lpHeader) + lpHeader->cb))
{
//**********************************************
// Format assumption:
// The bytes immediately preceding a POLYCURVE
// structure contain a valid POINTFX.
//
// If this is first curve, this points to the
// pfxStart of the POLYGONHEADER.
// Otherwise, this points to the last point of
// the previous POLYCURVE.
//
// In either case, this is representative of the
// previous curve's last point.
//**********************************************
ptStart = *(LPPOINTFX)((LPSTR)lpCurve - sizeof(POINTFX));
if (lpCurve->wType == TT_PRIM_LINE)
{
// convert the line segments to Bezier segments
cTotal += AppendPolyLineToBezier( &pt[cTotal], ptStart, lpCurve );
i = lpCurve->cpfx;
}
else if (lpCurve->wType == TT_PRIM_QSPLINE)
{
// Decode each Quadratic B-Spline segment, convert to bezier,
// and append to the Bezier segments
cTotal += AppendQuadBSplineToBezier( &pt[cTotal], ptStart, lpCurve );
i = lpCurve->cpfx;
}
else
// Oops! A POLYCURVE format we don't understand.
; // error, error, error
// Move on to next curve in the contour.
lpCurve = (LPTTPOLYCURVE)&(lpCurve->apfx[i]);
}
// Add points to close the contour.
// All contours are implied closed by TrueType definition.
// Depending on the specific font and glyph being used, these
// may not always be needed.
if ( pt[cTotal-1].x != pt[0].x || pt[cTotal-1].y != pt[0].y )
{
cTotal += CloseContour( pt, cTotal );
}
// flip coordinates to get glyph right side up (Windows coordinates)
// TT native coordiantes are zero originate at lower-left.
// Windows MM_TEXT are zero originate at upper-left.
for (i = 0; i < cTotal; i++)
pt[i].y = 0 - pt[i].y;
// Draw the contour
PolyBezier( hDC, pt, cTotal );
}
else
// Bad, bail, must have a bogus buffer.
break; // error, error, error
// Move on to next Contour.
// Its header starts immediate after this contour
lpHeader = (LPTTPOLYGONHEADER)(((LPSTR)lpHeader) + lpHeader->cb);
}
free( pt );
}

For more information on the TrueType specification please see:

Microsoft TrueType Specifications (http://www.microsoft.com/typography/tt/tt.htm)
(http://www.microsoft.com/typography/tt/tt.htm)

Also available on the Microsoft Developer Network Library CD's under Specifications.

Also available on the Microsoft Developer Network Library CD's under Specifications.

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