Yoshiyuki Kokojima
Toshiba Corp.
Research & Development Center

            
       
Kaoru Sugita
Toshiba Corp.
Research & Development Center

Takahiro Saito
Toshiba Corp.
Semiconductor Company

Takashi Takemoto
Toshiba Corp.
Semiconductor Company

  
Resolution independent rendering is important for many applications such as text rendering and rendering vector images. This area
has received quite some interest in recent years due to the growing popularity of Flash and SVG-based applications. This sketch
presents a new method for resolution independent rendering of vector images suitable for programmable graphics hardware. We have
enhanced a previous method [Loop and Blinn 2005] by using a stencil buffer and transparency multisampling [ATI 2005; NVI 2004],
so that our method has the following advantages:
¯ efficient rendering of dynamically deformable geometry,
¯ improved handling of geometric (self) intersections,
¯ order independent rendering with anti-aliasing.

(a)

(c)

(b)

 
We assume that a given vector object is defined by closed paths consisting of vector primitives such as line segments and Bézier curves,
see Figure 1(a). In this figure, filled dots represent the end points
of the vector primitives, and hollow dots represent Bézier control
points. This figure contains only quadratic curves for simplicity,
but our method is also able to handle cubic curves. Our method
consists of the following steps (see Figure 2):

(d)
(e)
(f)
Figure 1: Example of generating a stencil mask.

Triangulation
Curve-Edged
Triangles
(Figure 1(c))

1. Triangulation: Line-edged triangle fans (Figure 1(b)) are generated from the given vector object, each of which is defined by
the arbitrarily selected pivot point (each hollow box in Figure 1(b))
and the filled dots of the individual closed path. In addition, curveedged triangles (Figure 1(c)) are also generated by connecting the
end points and the control point of each Bézier curve.
2. Stencil buffer processing: A stencil buffer is cleared to zero,
and the line-edged triangle fans (Figure 1(b)) are drawn into the
buffer using a bitwise-inversion operator such as GL INVERT. If
a pixel is covered an odd number of times by the triangle fans,
its stencil value will be nonzero (black), otherwise zero (white),
as shown in Figure 1(d). Subsequently, the convex regions in the
curve-edged triangles (Figure 1(e)) are drawn into the stencil buffer,
which changes the content of the stencil buffer from Figure 1(d) to
Figure 1(f). We determine if a pixel is inside or outside the convex
region by evaluating an implicit equation [Loop and Blinn 2005] in
a pixel shader program.
3. Alpha assignment: Our method uses multisampling for antialiasing. However, aliasing artifacts on the curved edges remain
since multisampling does not anti-alias inside triangles [ATI 2005].
In order to reduce these artifacts, we assign alpha values to pixels
close to the curved edges using a signed distance function [Loop
and Blinn 2005]. These alpha values will be used for calculating
fragment coverage values in step 5.
4. Color buffer processing: A polygon large enough to enclose the
whole region of the given vector object is drawn into a color buffer
with a stencil mask that accepts fragments only where the stencil
buffer is nonzero.
5. Alpha to coverage: For anti-aliasing of the curved edges, we
map the alpha values assigned in step 3 to the coverage values using
transparency multisampling.





The previous method employed constrained Delaunay triangulation
and subdivision of overlapping triangles as preprocesses on a CPU.
 e-mail:

yoshiyuki.kokojima@toshiba.co.jp

Line-Edged
Triangle Fans
(Figure 1(b))

Vector
Object
(Figure 1(a))

CPU Process

Stencil
Image
(Figure
1(f))
Stencil Buffer
Processing

Alpha
Assignment

Alpha
Image

Color Buffer
Processing

Alpha to
Coverage

GPU Process

Figure 2: The process flow of our method.
If the given vector objects are deformed dynamically, the performance of the previous method will degrade since further CPU intervention is needed for re-triangulation and re-subdivision. In contrast, our method has no expensive CPU processes, and therefore it
can render dynamically deformable vector objects efficiently.
Another issue for the previous method is that the subdivision may
not terminate if the given objects have (self) intersections. Even
for such cases, our method guarantees termination of the processes
since the subdivision is unnecessary.
For anti-aliasing, the previous method employed alpha blending.
Thus, it was necessary to sort all the objects from back to front
since the result of alpha blending depends on a drawing order. In
contrast, our method uses transparency multisampling instead of
alpha blending. Therefore, sorting is unnecessary.



 

We applied our method to rendering of Japanese TrueType font outlines embedded in a three dimensional space. Our method rendered
over three hundred dynamically deforming characters at about 40
fps. Under such conditions, our method was more than 10 times
faster compared to the previous method.

 
ATI TECHNOLOGIES INC. 2005. Alpha to coverage, Radeon SDK
Mar. 2006.
LOOP, C., AND BLINN, J. 2005. Resolution independent curve rendering using programmable graphics hardware. In Proceedings of
SIGGRAPH 2005, 1000-1010.
Antialiasing with Transparency,
NVIDIA INC. 2004.
http://developer.nvidia.com/object/transparency aa.html.