Resolution Independent SVG-embedded Mesh Shading Framework

Paper Appendix Revision summary

Abstract

It is desirable to shade 3D objects with Scalable Vector Graphics (SVG) images for compactness and resolution independence.
However, huge programming complexity and high rendering cost limit SVG texturing techniques in rendering effectiveness.
This study overcomes these limitations by embeding SVG images into objects for resolution independent shading and efficient memory usage.
Our system decomposes paths of a SVG image into path segments of distinct uniform coloring operations without overlapping among their convex hulls for object retriangulation and samples colors into a 1D coloring texture.
Then, the segment and color information is computed and embedded into the triangle vertices.
Additionally, stroking paths are transformed to a set of line control vertices based on their intersection with the original mesh.
During rendering, two coloring pixel shaders compute pixel colors based on the embedded information and 1D coloring texture, and a stroking geometry shader sweeps point sprites of controlled widths along the stroking segments computed based on line control vertices to avoid costly distance computation.
Our SVG-embedded framework is efficient and simple without complex loop and branch structures for infinite texturing resolution as demonstrated in the results.

Video

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********** Introduction Video: ****************
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Video Download link

Result

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********** Result: Spiderman ******************
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Video Download link

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********** Result: bunny **********************
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Video Download link

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********** Result: Zebra **********************
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Video Download link

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********** Result: Kofu Tiger *****************
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********** Result: Cloth Simulation ***********
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Video Download link

Cloth Simulation

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****************** Loop's *********************
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Bunny

Video Download link

Sonic

Video Download link

Tigress

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Tiger

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Timing and Memory Statistics

	Int.(ms)	Imp.(ms)	Remesh(ms)	Tex.(ms)	Emb.(ms)
Spider	3150	0.30	22230	0.14	0.02
Spider(S)	755	0.25	2483	3.62	0.01
Bunny	1268	0.71	27261	0.14	0.03
Jacket	192	0.45	1053	0.15	0.01
Lego	76	0.46	2670	0.11	0.01
Cloth	13984	0.99	117761	0.13	0.07
Zebra	7964	0.48	87831	0.10	0.04
Tigress	4464	0.45	44268	0.16	0.02

● This shows the timing statistics when using our algorithm for Spiderman, Spiderman using stroking paths, Stanford bunny, Sonic of Jacket, Lego, Tiger Cloth, Zebra, and Tigress. Int. denotes the stage of path intersection and segment, Imp. denotes the stage of path implicitization, Remesh denotes the stage of constrained retriangulation, Tex. denotes the stage of coloring texture construction, and Emb. denotes the stage of embedding coloring information.

	Org.	Ours	Loop's	Resolution	Mem.(MB)
Spider	2584	33236	38774	820 X 820	(2.10,2.02)
Spider(S)	2584	7884	13328	320 X 320	(0.39,0.39)
Bunny	69630	88667	1621953	340 X 340 X 3	(2.99,2.99)
Jacket	2168	9951	19188	350 X 250	(0.34,0.33)
Lego	19034	29853	98130	160 X 160 X 2	(0.69,0.68)
Cloth	175118	216455	3763921	790 X 790	(6.85,6.85)
Zebra	40310	89861	207695	926 X 926	(3.54,3.53)
Tigress	5688	34781	98018	724 X 724	(1.73,1.73)

● This shows the memory usage statistics for both vector-based embedment and raster texturing for Spiderman, Spiderman using stroking paths, Stanford bunny, Sonic of Jacket, Lego, Tiger Cloth, Zebra, and Tigress. Org. is the number of triangles in the original mesh, Ours is the number of triangles in the retriangulated mesh using our algorithm, Loop's is the number of triangles in the retriangulated mesh using Loop's method, Resolution is the resolution of the corresponding rasterization texture, and Mem. is the memory usage for the raster texturing and our embedded shading techniques. For raster texturing, the required memory usage contains the texture images and original mesh including vertex positions, normals, and texture coordinates, and face indices. For our shading, the required memory usage contains the retriagulated mesh, embedded coloring and stroking information, and coloring texture in GPU for the model.

	Fragment(ms)	Geometry(ms)	Normal(FPS)		Zoom In(FPS)		Zoom Out(FPS)
			Ours	Loop's	Ours	Loop's	Ours	Loop's
Spider	1.4	0	448	99	84	48	756	308
Spider(S)	1.05	7.7	151	56	67	19	223	78
Bunny	4.7	4	149	19	73	7	174	37
Jacket	1.2	0.7	223	56	52	24	496	87
Lego	0.75	0	101	33	44	21	198	88
Cloth	0.75	9.8	56	9	34	6	73	11
Zebra	0.75	0	371	69	109	47	794	204
Tigress	0.75	0	307	35	70	12	469	83

● This shows the timing statistics for Spiderman, Spiderman using stroking paths, Stanford bunny, Sonic of Jacket, Lego, Tiger Cloth, Zebra, and Tigress. Fragment is the timing in (ms) required to shade a texturing object with the coloring pixel shader, Geomtry is the timing in (ms) required to shade a texturing object with the stroking geometry shader, Normal is the overall frame rate for shading an object when viewing it fully, Zoom In is the overall frame rate for shading an object when zooming in to view parts of the model, and Zoom Out is the overall frame rate for shading an object when zooming out to have the model occupy half of the window. Ours is the frame rate for shading with our algorithm and Loop's is the frame rate for shading with our implemented Loop's algorithm with antialiasing. Please notice the frame rate is measured when turning off the GPU antialiasing function.

Compare to Nehab2008

	Plane(Nehab's)			Plane(Ours)
	Normal	Zoom	Mem.(MB)	Normal	Zoom	Mem.(MB)
Butterfly	35	18	9	71	68	13
Dancer	65	17	6	86	69	11
Skater	52	18	8	87	70	12
Lion	56	18	8	73	66	11
Tiger	45	18	10	67	47	19

● This shows the timing statistics in FPS when comparing our algorithm with Nehab's algorithm using the data set and code posted in their paper. All data is collected in the resolution of 1920x1080 with the GPU antialiasing function turning on. Normal and Zoom are the view of having the entire object fitting inside the screen and zooming view of the details. Plane denotes texturing a plane and Cylinder denotes texturing a cylinder. Ours denotes the use of our algorithm and Nehab's denote the use of the one proposed by Nehab. Antialiasing can largely reduce the frame rate. For example, shading the Butterfly plane with Nehab's algorithm on plane has a frame rate of 250/35 without/with antialiasing.

Compare to Loop2005

SpiderMan

	oriTris.	reTris.	Ce.(Mem)	It.(Mem)	Memory(MB)
Layer1	2584	4728	424(0.06)	12912(1.08)	1.14
Layer2	2584	31462	6608(0.87)	24854(2.09)	2.96
Layer3	2584	2584	0(0.00)	7752(0.65)	0.65
Total		38774	7032(0.93)	45518(3.82)	4.75

● This shows the comparison with our algorithm and the method of Loop's for Spiderman.
oriTris. denotes the number of triangles of original mesh, reTris. denotes the number of triangles of the retriangulated mesh, Ce. denotes the number of curve embedded triangles of the retriangulated mesh, It. denotes the number of interior triangles of the retriangulated mesh, and Memory denotes the memory usage each layer.

Bunny

	oriTris.	reTris.	Ce.(Mem)	It.(Mem)	Memory(MB)
Layer1	69630	70457	140(0.02)	70317(5.91)	5.93
Layer2	69630	70606	142(0.02)	70464(5.92)	5.94
Layer3	69630	70725	257(0.03)	70468(5.92)	5.95
Layer4	69630	70278	116(0.02)	70162(5.89)	5.91
Layer5	69630	70237	139(0.02)	70098(5.89)	5.91
Layer6	69630	70859	241(0.03)	70618(5.93)	5.96
Layer7	69630	69936	86(0.01)	69850(5.87)	5.88
Layer8	69630	70082	123(0.02)	69959(5.88)	5.90
Layer9	69630	73018	721(0.10)	72297(6.07)	6.17
Layer10	69630	71058	314(0.04)	70744(5.94)	5.98
Layer11	69630	71591	413(0.05)	71178(5.98)	6.03
Layer12	69630	70084	41(0.01)	70043(5.88)	5.89
Layer13	69630	72872	832(0.11)	72040(6.05)	6.16
Layer14	69630	69702	14(0.00)	69688(5.85)	5.85
Layer15	69630	69736	18(0.00)	69718(5.86)	5.86
Layer16	69630	69867	64(0.01)	69803(5.86)	5.87
Layer17	69630	70083	95(0.01)	69988(5.88)	5.89
Layer18	69630	69861	51(0.01)	69810(5.86)	5.87
Layer19	69630	70172	46(0.01)	70126(5.89)	5.90
Layer20	69630	70022	92(0.01)	69930(5.87)	5.88
Layer21	69630	69962	28(0.00)	69934(5.87)	5.87
Layer22	69630	70766	132(0.02)	70634(5.93)	5.95
Layer23	69630	69979	115(0.02)	69864(5.87)	5.89
Total		1621953	4220(0.56)	1617733(135)	136

● This shows the comparison with our algorithm and the method of Loop's for Stanford bunny.
oriTris. denotes the number of triangles of original mesh, reTris. denotes the number of triangles of the retriangulated mesh, Ce. denotes the number of curve embedded triangles of the retriangulated mesh, It. denotes the number of interior triangles of the retriangulated mesh, and Memory denotes the memory usage each layer.

Sonic

	oriTris.	reTris.	Ce.(Mem)	It.(Mem)	Memory(MB)
Layer1	2168	2390	50(0.01)	2340(0.19)	0.20
Layer2	2168	2978	187(0.02)	2791(0.24)	0.26
Layer3	2168	3302	260(0.03)	3042(0.26)	0.29
Layer4	2168	2725	142(0.02)	2583(0.22)	0.24
Layer5	2168	3058	235(0.03)	2823(0.24)	0.27
Layer6	2168	2433	63(0.01)	2370(0.20)	0.21
Layer7	2168	2302	31(0.00)	2271(0.19)	0.19
Total		19188	968(0.13)	18220(1.53)	1.66

● This shows the comparison with our algorithm and the method of Loop's for Sonic of Jacket.
oriTris. denotes the number of triangles of original mesh, reTris. denotes the number of triangles of the retriangulated mesh, Ce. denotes the number of curve embedded triangles of the retriangulated mesh, It. denotes the number of interior triangles of the retriangulated mesh, and Memory denotes the memory usage each layer.

Lego

	oriTris.	reTris.	Ce.(Mem)	It.(Mem)	Memory(MB)
Layer1	19034	19034	0(0.00)	19034(1.60)	1.60
Layer2	19034	20240	256(0.03)	19984(1.68)	1.71
Layer3	19034	19538	112(0.02)	19426(1.63)	1.65
Layer4	19034	19106	24(0.00)	19082(1.60)	1.60
Layer5	19034	20212	239(0.03)	19973(1.68)	1.71
Total		98130	631(0.08)	97499(8.19)	8.27

● This shows the comparison with our algorithm and the method of Loop's for Lego.
oriTris. denotes the number of triangles of original mesh, reTris. denotes the number of triangles of the retriangulated mesh, Ce. denotes the number of curve embedded triangles of the retriangulated mesh, It. denotes the number of interior triangles of the retriangulated mesh, and Memory denotes the memory usage each layer.

Tiger Cloth

	oriTris.	reTris.	Ce.(Mem)	It.(Mem)	Memory(MB)
Layer1	175118	179042	554(0.07)	178488(15.0)	15.1
Layer2	175118	176343	129(0.02)	176214(14.8)	14.8
Layer3	175118	176818	199(0.03)	176619(14.8)	14.8
Layer4	175118	176820	190(0.03)	176630(14.8)	14.8
Layer5	175118	176882	195(0.03)	176687(14.8)	14.8
Layer6	175118	176852	191(0.03)	176661(14.8)	14.8
Layer7	175118	176887	204(0.03)	176683(14.8)	14.8
Layer8	175118	176587	140(0.02)	176447(14.8)	14.8
Layer9	175118	176481	127(0.02)	176354(14.8)	14.8
Layer10	175118	176621	168(0.02)	176453(14.8)	14.8
Layer11	175118	177039	201(0.03)	176838(14.9)	14.9
Layer12	175118	176485	146(0.02)	176339(14.8)	14.8
Layer13	175118	176406	140(0.02)	176266(14.8)	14.8
Layer14	175118	176302	109(0.01)	176193(14.8)	14.8
Layer15	175118	186155	2291(0.30)	183864(15.4)	15.7
Layer16	175118	181490	1006(0.13)	180484(15.2)	15.3
Layer17	175118	175963	114(0.02)	175849(14.8)	14.8
Layer18	175118	177044	410(0.05)	176634(14.8)	14.9
Layer19	175118	175673	82(0.01)	175591(14.7)	14.7
Layer20	175118	175388	30(0.00)	175358(14.7)	14.7
Layer21	175118	216643	6463(0.85)	210180(17.7)	18.6
Total		3763921	13089(1.73)	3750832(315)	317

● his shows the comparison with our algorithm and the method of Loop's for Tiger Cloth.
oriTris. denotes the number of triangles of original mesh, reTris. denotes the number of triangles of the retriangulated mesh, Ce. denotes the number of curve embedded triangles of the retriangulated mesh, It. denotes the number of interior triangles of the retriangulated mesh, and Memory denotes the memory usage each layer.

Zebra

	oriTris.	reTris.	Ce.(Mem)	It.(Mem)	Memory(MB)
Layer1	40310	78738	3196(0.42)	75542(6.35)	6.77
Layer2	40310	82737	3377(0.45)	79360(6.67)	7.12
Layer3	40310	46220	923(0.12)	45297(3.80)	3.92
Total		207695	7496(0.99)	200199(16.8)	17.8

● This shows the comparison with our algorithm and the method of Loop's for Zebra.
oriTris. denotes the number of triangles of original mesh, reTris. denotes the number of triangles of the retriangulated mesh, Ce. denotes the number of curve embedded triangles of the retriangulated mesh, It. denotes the number of interior triangles of the retriangulated mesh, and Memory denotes the memory usage each layer.

Tigress

	oriTris.	reTris.	Ce.(Mem)	It.(Mem)	Memory(MB)
Layer1	5688	14744	1936(0.26)	12808(1.08)	1.34
Layer2	5688	10437	1086(0.14)	9351(0.79)	0.93
Layer3	5688	8340	747(0.10)	7593(0.64)	0.74
Layer4	5688	15332	2175(0.29)	13157(1.11)	1.40
Layer5	5688	8170	501(0.07)	7669(0.64)	0.71
Layer6	5688	12276	1347(0.18)	10929(0.92)	1.10
Layer7	5688	8861	546(0.07)	8315(0.70)	0.77
Layer8	5688	7362	117(0.02)	7245(0.61)	0.63
Layer9	5688	6520	120(0.02)	6400(0.54)	0.56
Layer10	5688	5976	44(0.01)	5932(0.50)	0.51
Total		98018	8619(1.14)	89399(7.51)	8.65

● This shows the comparison with our algorithm and the method of Loop's for Tigress.
oriTris. denotes the number of triangles of original mesh, reTris. denotes the number of triangles of the retriangulated mesh, Ce. denotes the number of curve embedded triangles of the retriangulated mesh, It. denotes the number of interior triangles of the retriangulated mesh, and Memory denotes the memory usage each layer.