ksheng- / fast-differentiable-rasterizer

differentiable bezier curve rasterizer with PyTorch

fast-differentiable-rasterizer

Background

pathfinder
NV_path_rendering

Preliminary performance testing

Machine specs

MacBook: 2.2 GHz 2 core Broadwell i7, 8GB RAM, no GPU
GCP n1-standard-8 VM : 2.2 GHz 8 vCPU Broadwell E5, 30GB RAM, Tesla V100

Algorithm	MacBook	GCP VM
naive	0.965s	0.405s

Experiments

GCP n1-standard-8 (2.2 GHz / 8 core Broadwell, 30GB RAM) instance with Tesla V100 PyTorch 1.0.0 running with Python 3.7, CUDA 9.0, cuDNN 7.1 res=512, steps=128

Algorithm:

• Sample parametric curve at fixed number of points (doing this recursively until we have each pixel is similar to de Castlejau, but we're approximately for efficiency. Its worth noting that points will "bunch up" at tighter points on this curve.
• At this point, we could use Bresenham style techniques / other line drawing primitives to connect these points with straight lines (or even horizontal/vertical lines if we have enough points).
• However, thats an inherently sequential and discrete algorithm that works on a pixel by pixel basis. Instead we're going to draw a bivariate Gaussian at each point and superimpose them to get our differentiable raster.

Test 1: ms/iter, quadratic curve (100 passes)

python bezier.py --passes 100 --method [--disable-cuda]

method	forward	backward	total	speedup	peak_mem
base	414.9 ms	448.4 ms	863.3 ms	1.00x	N/A
cuda	3.1 ms	5.7 ms	8.8 ms	98.10x	942 MB
half	2.7 ms	3.6 ms	6.3 ms	137.03x	472 MB
bounded	1.9 ms	2.5 ms	4.3 ms	196.20x	245 MB
tiled	9.4 ms	2.0 ms	11.4 ms	75.73x	153 MB
shrunk_cpu	16.2 ms	142.5 ms	158.7 ms	5.44x	N/A
shrunk_cuda	18.3 ms	22.9 ms	41.2 ms	20.95x	8 MB

Test 2: ms/iter cubic curve (100 passes)

python bezier.py --passes 100 --draw cubic --method [--disable-cuda]

method	forward	backward	total	speedup	peak_mem
base	418.4 ms	449.0 ms	867.4 ms	1.00x	N/A
cuda	3.3 ms	6.1 ms	9.4 ms	92.28x	942 MB
half	2.9 ms	4.0 ms	6.9 ms	125.71x	472 MB
bounded	2.9 ms	4.2 ms	7.1 ms	122.17x	472 MB
tiled	10.4 ms	2.3 ms	12.7 ms	68.30x	148 MB
shrunk_cuda	18.2 ms	22.9 ms	41.1 ms	21.10x	8 MB

comments: interpolation is cheap (number of points does not increase, but spacial coverage does)

Test 3: ms/iter 3 section composite quadratic curve (100 passes)

python bezier.py --passes 100 --draw char --method [--disable-cuda]

method	forward	backward	total	speedup	peak_mem
base	1131.9 ms	1217.5 ms	2349.4 ms	1.00x	N/A
cuda	8.9 ms	15.8 ms	24.7 ms	95.12x	2821 MB
half	7.4 ms	9.4 ms	16.8 ms	139.85x	1412 MB
bounded	5.3 ms	7.9 ms	13.2 ms	177.98x	1053 MB
tiled	20.1 ms	2.7 ms	22.8 ms	130.04x	434 MB
shrunk_cpu	48.8 ms	383.8 ms	432.6 ms	5.43x	N/A
shrunk_cuda	55.9 ms	69.7 ms	125.6 ms	18.71x	15 MB

Test 4: ms/iter 16 section composite quadratic curve (100 passes)

NOT UP TO DATE python bezier.py --passes 100 --batch 16 --method [--disable-cuda]

method	forward	backward	total	speedup	peak_mem
base	414.9 ms	448.4 ms	863.3 ms	1.00x	N/A
cuda	0.6 ms	5.7 ms	6.3 ms	137.03x	942 MB
half	0.8 ms	4.1 ms	4.9 ms	176.18x	607 MB
bounded	2.5 ms	3.3 ms	5.8 ms	148.84x	486 MB
tiled	15.2 ms	13.1 ms	28.3 ms	30.51x	347 MB
shrunk_cpu	16.2 ms	142.5 ms	158.7 ms	5.44x	N/A
shrunk_cuda	18.3 ms	22.9 ms	41.2 ms	20.95x	8 MB

Test 5: ms/iter vs num_curves

python bezier.py --passes 100 --batch <num_curves> --method [--disable-cuda]

num_curves	base	half	tiled
2	1.6 s	12.7 ms	17.7 ms
4	3.3 s	22.8 ms	27.0 ms
8	6.3 s	43.4 ms	47.1 ms
16	12.9 s	86.4 ms	80.4 ms
32	26.1 s	168.9 ms	163.8 ms

Test 6: max_memory_allocated vs num_curves

python bezier.py --passes 100 --batch <num_curves> --method

num_curves	half	tiled
2	0.9 GB	0.3 GB
4	1.9 GB	0.6 GB
8	3.8 GB	1.2 GB
16	7.5 GB	2.4 GB
32	15.0 GB	4.8 GB

Test 7: Snakeviz / profiler output