Exponential Shadow Maps

Transcription

1 Exponential Shadow Maps Matthijs Venselaar, Ingo van Duijn Universiteit Utrecht March 28, 2013 Matthijs Venselaar, Ingo van Duijn (UU) Exponential Shadow Maps March 28, / 17

2 Shadow Maps Exponential Shadow Mapping allows filtered shadow maps. Matthijs Venselaar, Ingo van Duijn (UU) Exponential Shadow Maps March 28, / 17

3 Shadow Maps Shadow test f (d, z) = { 1 if d z 0 otherwise f shadow function d depth from point to light z sampled shadow map value Binary-valued shadow function determines if a point is lit Point is always fully lit or fully dark Even when using a pre-filtered shadow map! This causes artifacts Matthijs Venselaar, Ingo van Duijn (UU) Exponential Shadow Maps March 28, / 17

4 Filtering the Shadow Map Conceptually simplest way to filter the shadow map is PCF Percentage Closer Filter Average multiple shadow tests with different z values: average(f (d, z)) However, more samples yield high bandwidth usage. We want: Apply regular texture filters on shadow map Calculate a value f (d, z) [0, 1] with just one sample While retaining real-time performance! Matthijs Venselaar, Ingo van Duijn (UU) Exponential Shadow Maps March 28, / 17

5 Linearising the Shadow Function Observation Each object is either occluder (d = z) or occluded (d > z), so in theory: d z Model the shadow function as the limit of an exponential function: f (d, z) = lim α e α(d z) Matthijs Venselaar, Ingo van Duijn (UU) Exponential Shadow Maps March 28, / 17

6 Exponential Shadow Function A larger α in e α(d z) models the binary shadow function better. Float precision imposes upper bound on α. Separated exponential function Separate the pre-calculated values z from the yet unknown value d: f (d, z) = e α(d z) = e αd e αz Matthijs Venselaar, Ingo van Duijn (UU) Exponential Shadow Maps March 28, / 17

7 Key Insight Somehow pre-filter known shadow map values z(p). Represent filtering operation by convolving with a kernel w. Filter as convolution s f (x) = [w f (d(x), z)](p) = [w e αd(x) e αz ](p) = e αd(x) [w e αz ](p) NB. this means we store e αz in a texture and pre-filter it! Matthijs Venselaar, Ingo van Duijn (UU) Exponential Shadow Maps March 28, / 17

8 New Shadow Test as Exponential Function Shadow test f (d, t) = e αd t f exponential shadow function d depth from point to light t filtered shadow map value We can: Filter the shadow map any way we like Get a value f (d, t) [0, 1] with one sample Without extensive computations or many samples Matthijs Venselaar, Ingo van Duijn (UU) Exponential Shadow Maps March 28, / 17

9 Variance Shadow Maps Shadow map method using probability theory Also allows texture filtering Suffers from light bleeding Matthijs Venselaar, Ingo van Duijn (UU) Exponential Shadow Maps March 28, / 17

10 ESM vs. VSM Matthijs Venselaar, Ingo van Duijn (UU) Exponential Shadow Maps March 28, / 17

11 Artifacts Remember the assumption: d z Sometimes violated Float arithmetic Special cases Possible to classify violations Fall back on other solution (e.g. PCF ) Matthijs Venselaar, Ingo van Duijn (UU) Exponential Shadow Maps March 28, / 17

12 Artifacts Red pixels violate the assumption that d z Matthijs Venselaar, Ingo van Duijn (UU) Exponential Shadow Maps March 28, / 17

13 Classification of Violations Red pixels violate assumption Relatively few violations Not very costly to fall back on more expensive method Matthijs Venselaar, Ingo van Duijn (UU) Exponential Shadow Maps March 28, / 17

14 Comparison Basic SM VSM ESM Texture filter No Yes Yes Artifacts Shadow Acne Light Bleeding Fall back method Floats/texel ESM is not perfect. Still suffers from similar problems But overall much less Matthijs Venselaar, Ingo van Duijn (UU) Exponential Shadow Maps March 28, / 17

15 Exponential Variance Shadow Map Very easy to combine ESM and VSM into EVSM VSM uses z and z 2 But can use e αz and e 2αz just as well Better bound on Chebychev s inequality But needs more memory than ESM Only fails where both ESM and VSM fails Combination of techniques is possible, but there is always a trade-off between performance and quality. Matthijs Venselaar, Ingo van Duijn (UU) Exponential Shadow Maps March 28, / 17

16 Conclusions Texture pre-filtering made possible Do not store z value, but e αz Handles light bleeding better than VSM Fast and memory efficient Can easily be combined with other approach (e.g EVSM) Matthijs Venselaar, Ingo van Duijn (UU) Exponential Shadow Maps March 28, / 17

17 References Thomas Annen, Tom Mertens, Hans-Peter Seidel, Eddy Flerackers, Jan Kautz Exponential Shadow Maps. Proceedings of graphics interface 2008, Matthijs Venselaar, Ingo van Duijn (UU) Exponential Shadow Maps March 28, / 17