Academia.eduAcademia.edu

Figure 9 – uploaded by Frank Dachille

See full PDFdownloadDownload figure
Fig. 9. Comparison between Footprint Assembly and Feline: (a) screen space, (b) texture space of Footprint Assembly, (c) and Feline

Figure 9 Comparison between Footprint Assembly and Feline: (a) screen space, (b) texture space of Footprint Assembly, (c) and Feline

Related Figures (16)

Fig. 1. Four regions of a texture mapped checkerboard plane magnification (cyan), minification (red), and mixed regions (green anc blue).
Fig. 1. Four regions of a texture mapped checkerboard plane magnification (cyan), minification (red), and mixed regions (green anc blue).
Fig. 3. No texel may be projected into a pixel footprint in naive forwar point projection methods.
Fig. 3. No texel may be projected into a pixel footprint in naive forwar point projection methods.
Fig. 2. Forward projected texel footprint may cover no pixels in naive forward footprint projection methods.
Fig. 2. Forward projected texel footprint may cover no pixels in naive forward footprint projection methods.
Fig. 4. Forward point projection texture filtering with (a) backward bilinear interpolation to fill in the holes [10] (notice aliasing due to subsampling in one direction) and (b) our solution with supersampling in texture space to fill in the holes. (c) and (d) are zoom-ins of the marked rectangles of (a) and (b), respectively.
Fig. 4. Forward point projection texture filtering with (a) backward bilinear interpolation to fill in the holes [10] (notice aliasing due to subsampling in one direction) and (b) our solution with supersampling in texture space to fill in the holes. (c) and (d) are zoom-ins of the marked rectangles of (a) and (b), respectively.
Fig. 5. The backward projected footprint may cover no texels in naive backward footprint projection methods.
Fig. 5. The backward projected footprint may cover no texels in naive backward footprint projection methods.
Fig. 6. Solutions to the undersampling problem in backward footprint projection: (a) overblurred EWA [15] and (b) out clamping method. (c) and (d) are zoom-ins of the marked rectangles of (a) and (b), respectively.
Fig. 6. Solutions to the undersampling problem in backward footprint projection: (a) overblurred EWA [15] and (b) out clamping method. (c) and (d) are zoom-ins of the marked rectangles of (a) and (b), respectively.
Fig. 7. The minor axis is over supersampled in naive backward poin projection methods.
Fig. 7. The minor axis is over supersampled in naive backward poin projection methods.
Fig. 8. Prefiltering methods: (a) MIP-mapping; (b) Footprint Assembly/ Feline.
Fig. 8. Prefiltering methods: (a) MIP-mapping; (b) Footprint Assembly/ Feline.
To hold the partial contribution of all subpixels during the scanline processing, intuitively, two scanline buffers are required: one for the current scanline L; and another for the next scanline L;,,. But, for a compact implementation, a scanline buffer of size length +1 working as a FIFO is sufficient, where length is the length of the scanline. Once the final colors are produced for pixels in scanline L;, their memory can be immediately released for storing the partial colors of pixels in scanline L;.;. Each pixel of the scanline buffer stores the accumulated color RGB and weight. The (u,v) coordinates in texture space are also stored in the buffer. This is used for pixel vector calculation, to be discussed in the next section. Since the operations are conducted in two MIP-map levels, hence, two sets of buffers are needed, resulting in two scanline buffers. This is still feasible for hardware implementation if we use bucket When the pixel coverage overlaps, subpixels between neighboring pixels contribute to all surrounding pixels. For example, in Fig. 11a, subpixels within the square region aefg contribute to pixels a, e, f, and g. The naive implementation of our adaptive sampling method (Section 2.4) calculates the subpixels of each pixel sepa- rately, which means that the subpixels are calculated four times. This requires not only costly computation, but also a high memory bandwidth. To address this issue, coherence
To hold the partial contribution of all subpixels during the scanline processing, intuitively, two scanline buffers are required: one for the current scanline L; and another for the next scanline L;,,. But, for a compact implementation, a scanline buffer of size length +1 working as a FIFO is sufficient, where length is the length of the scanline. Once the final colors are produced for pixels in scanline L;, their memory can be immediately released for storing the partial colors of pixels in scanline L;.;. Each pixel of the scanline buffer stores the accumulated color RGB and weight. The (u,v) coordinates in texture space are also stored in the buffer. This is used for pixel vector calculation, to be discussed in the next section. Since the operations are conducted in two MIP-map levels, hence, two sets of buffers are needed, resulting in two scanline buffers. This is still feasible for hardware implementation if we use bucket When the pixel coverage overlaps, subpixels between neighboring pixels contribute to all surrounding pixels. For example, in Fig. 11a, subpixels within the square region aefg contribute to pixels a, e, f, and g. The naive implementation of our adaptive sampling method (Section 2.4) calculates the subpixels of each pixel sepa- rately, which means that the subpixels are calculated four times. This requires not only costly computation, but also a high memory bandwidth. To address this issue, coherence
rendering [19], in which the framebuffer is subdivided into coherent regions that are rendered independently (also known as tiled rendering or chunking). Bucket rendering enables a deeper working set memory to be kept on chip.
rendering [19], in which the framebuffer is subdivided into coherent regions that are rendered independently (also known as tiled rendering or chunking). Bucket rendering enables a deeper working set memory to be kept on chip.
The magnitude of the minor vector m can be approxi- mated by: of an additonal pixel to its right. However, note that, for these additional pixels, only their projections are calculated. The magnitudes of these vectors are approximated with: The minor vector m is used to compute the MIP level / and the scaling factor f of level I:
The magnitude of the minor vector m can be approxi- mated by: of an additonal pixel to its right. However, note that, for these additional pixels, only their projections are calculated. The magnitudes of these vectors are approximated with: The minor vector m is used to compute the MIP level / and the scaling factor f of level I:
Fig. 13. (a) Feline versus (b) our FAST area sampling. FAST area sampling method, the minor axis rz is used to determine the MIP-map level (5), which is 1 for this case. In level 1, the scaled two vectors become |r{| = 8.0 and \r5| = 1.2, respectively. The total sampling rate is deter- mined as N = [8.0 x 1.2] = 10. The number of samples in level 2 is N’ = [#7] = 3. In total, Feline spends 14 samples for the two MIP-map levels, while FAST spends 13 samples. Straightforward implementation of the adaptive sampling method creates the highest quality image with less blurring and better antialiasing (Fig. 14b). Utilizing coherence only in the adaptive sampling method (without prefiltering) promises the same high quality (Fig. 14c). Feline delivers better quality than MIP-mapping by introducing anisotro- pic filtering (Fig. 14d). This can be observed from the text image, but aliasing is still present in the checkerboard image. By setting the clamping factor to 4, the quality is similar (Fig. 14e). However, by further reducing the clamping factor to 2, the image becomes blurrier (Fig. 14f). Our FAST method, with coherence utilization, prefiltering, and the footprint area sampling scheme, creates images of indistinguishable quality as compared to straightforward adaptive sampling (Fig. 14g). By setting the clamping factor to 4, the quality is similar (Fig. 14h). However, by setting the clamping factor to 2, the image becomes a bit blurrier and more aliased (Fig. 14i). The difference can be seen more clearly from zoom-ins in Figs. 14j-l. The quality of animations is consistent with that of the extracted frames for each method.
Fig. 13. (a) Feline versus (b) our FAST area sampling. FAST area sampling method, the minor axis rz is used to determine the MIP-map level (5), which is 1 for this case. In level 1, the scaled two vectors become |r{| = 8.0 and \r5| = 1.2, respectively. The total sampling rate is deter- mined as N = [8.0 x 1.2] = 10. The number of samples in level 2 is N’ = [#7] = 3. In total, Feline spends 14 samples for the two MIP-map levels, while FAST spends 13 samples. Straightforward implementation of the adaptive sampling method creates the highest quality image with less blurring and better antialiasing (Fig. 14b). Utilizing coherence only in the adaptive sampling method (without prefiltering) promises the same high quality (Fig. 14c). Feline delivers better quality than MIP-mapping by introducing anisotro- pic filtering (Fig. 14d). This can be observed from the text image, but aliasing is still present in the checkerboard image. By setting the clamping factor to 4, the quality is similar (Fig. 14e). However, by further reducing the clamping factor to 2, the image becomes blurrier (Fig. 14f). Our FAST method, with coherence utilization, prefiltering, and the footprint area sampling scheme, creates images of indistinguishable quality as compared to straightforward adaptive sampling (Fig. 14g). By setting the clamping factor to 4, the quality is similar (Fig. 14h). However, by setting the clamping factor to 2, the image becomes a bit blurrier and more aliased (Fig. 14i). The difference can be seen more clearly from zoom-ins in Figs. 14j-l. The quality of animations is consistent with that of the extracted frames for each method.
Fig. 14. Texture mapping using (a) traditional MIP-map, (b) adaptive sampling without coherence, (c) adaptive sampling with coherence, (d) Feline without clamping, (e) Feling with clamp = 4, (f) Feline with clamp = 2, (g) FAST without clamping, (h) FAST with clamp = 4, (i) FAST with clamp = 2. (j), (kK), and (I) are zoom-ins of the marked racteangles of (a), (d) and (g), respectively.
Fig. 14. Texture mapping using (a) traditional MIP-map, (b) adaptive sampling without coherence, (c) adaptive sampling with coherence, (d) Feline without clamping, (e) Feling with clamp = 4, (f) Feline with clamp = 2, (g) FAST without clamping, (h) FAST with clamp = 4, (i) FAST with clamp = 2. (j), (kK), and (I) are zoom-ins of the marked racteangles of (a), (d) and (g), respectively.
Fig. 15. Average rendering time per pixel (milliseconds) for 110 frames of a room scene animation.
Fig. 15. Average rendering time per pixel (milliseconds) for 110 frames of a room scene animation.
Fig. 16. Number of sample points per pixel for 110 frames of a room scene animation.
Fig. 16. Number of sample points per pixel for 110 frames of a room scene animation.
Related topics:
AlgorithmsComputer GraphicsThree Dimensional ImagingInformation Storage and RetrievalImage EnhancementReproducibility of ResultsImage Textureimage resolution
580 California St., Suite 400
San Francisco, CA, 94104
© 2025 Academia. All rights reserved