Objective

2

An importance sampling method based on bidirectional reflectance distribution function (BRDF) has excellent fidelity when rendering the surface of an object. However

this sampling method has a complicated form and can lead to heavy hardware storage cost

which can cause many problems when applied to practical use. These problems include high implementation complexity

low execution efficiency

and high debugging difficulty. Owing to these problems

this study provides a new method for computing the reflection direction of a light path. The new method uses weight generation technique and vector linear interpolation. This method not only reduces the complexity of the algorithm but also reduces the computational complexity of many previous sampling algorithms. The new method is also easy to implement.

Method

2

The algorithm initially calculates the direction of reflected light and subsequently combines the features of cosine and exponential functions given the direction of incident light and surface normal. This algorithm generates a weight value that has a certain distribution characteristic. The algorithm defines a parameter called

ε

to enable the distribution characteristic to be controllable. The surface tends to exhibit a diffuse reflection for each incoming light ray when

ε

is relatively small. Otherwise

the surface tends to exhibit an ideal mirror reflection. The new algorithm performs a linear interpolation between a mirror and diffuse reflection directions to obtain a new vector after the weight generation process

and the weight that was generated previously was used in this process. Finally

the algorithm obtains the desired reflection direction of a light ray by normalizing the new vector. This method efficiently simulates glossy surfaces

which exist vastly in real life.

Result

2

This study conducts a full implementation of the path tracing algorithm. The new algorithm is based on the new sampling method described previously. Nine kinds of common surface materials are selected for the rendering test through this algorithm. Experimental results are compared with the actual results obtained by the original BRDF sampling algorithm. The original data size for the BRDF parameter of each actual surface is approximately 34 MB. Notably

storing the raw BRDF data when the scene contains various material surfaces is infeasible. The rendering speed can be increased by 1.521.99 times using the fast sampling algorithm

and the relative error caused by approximation can be controlled within 8%. Moreover

the original 34 MB data used to describe the surface of the object can be replaced by only storing few floating-point numbers

which can apparently reduce hardware storage overhead considerably. This sampling method has a low hardware storage cost

and its rendered picture can still retain a high degree of realism. These features are favorable for modern hardware that is specifically designed for solving high computational complexity problems but limited to memory bandwidth. The object being rendered can achieve a smooth transition from an ideal diffuse to specular reflection and ideal mirror reflection because a smoothness parameter changes continuously. Moreover

the new algorithm unifies the sampling method used in many path tracing renderers. These renderers frequently use different sampling models when rendering various types of material surfaces to improve rendering quality. This improvement will inevitably increase thread divergence when rendering and considerably reduce the operating efficiency of the rendering program. These drawbacks are particularly evident on parallel hardware

such as GPUs

and must be avoided to a feasible extent. Thus

this algorithm condenses different rendering models used by various types of renderers and obtains a unified sampling method

even when the material properties of the surface are relatively complex to render correctly. The algorithm can also be appropriately extended and approximated by a multilayer fitting technique to simulate the material properties of the rendered surface. The algorithm has favorable scalability and practicality.

Conclusion

2

This study uses a simplified algorithm to compute the exit direction of light to replace the traditional method used in path tracing renderers without sacrificing the authenticity of the rendered image. This study also fully implements the path tracing algorithm to enable its practical application. This algorithm can effectively simulate mirror

diffuse

and glossy reflection

has extensive applications when rendering various kinds of objects that exist in real life

and can be used as an alternative approach to replace existing sampling methods. This algorithm has a low storage overhead

which is an advantage when rendering complex scenes that contain various materials without consuming numerous memory resources. This algorithm also exhibits excellent performance when rendering common isotropic materials

such as rough or diffuse surfaces

porcelain

and metals.