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Mitsuba is a research-oriented rendering system in the style of PBRT, from which it derives much inspiration. It is written in portable C++, implements unbiased as well as biased techniques, and contains heavy optimizations targeted towards current CPU architectures.

In comparison to other open source renderers, Mitsuba places a strong emphasis on experimental rendering techniques, such as path-based formulations of Metropolis Light Transport and volumetric modeling approaches.

www.mitsuba-renderer.org

logo_luxrender

LuxRender is a rendering system for physically correct, unbiased image synthesis.
It supports both unbiased (MLT/(bidir)Path Tracing) and biased techniques (directlighting, photonmapping), physically correct light sources, advanced procedural textures, spectral light calculus, motion blur, lightgroup blending and tight integration with blender.

www.luxrender.net

logo_yafaray

Yafaray is a ray tracer, offering Global Illumination and Photon Mapping, for high quality photorealistic rendering.

www.yafaray.org

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Appleseed is an open source, physically-based global illumination rendering engine primarily designed for animation and visual effects.
Appleseed implements a modern workflow based on path tracing that enables artifact-free, single pass rendering with very little technical tuning. It is simultaneously capable of strictly unbiased rendering when total accuracy matters, and biased rendering when artistic freedom and shorter rendering time are paramount.

Appleseed supports fully programmable shading via Sony Pictures Imageworks Open Shading Language, RGB and spectral rendering, fast and robust transformation and deformation motion blur, state-of-the-art ray traced subsurface scattering, exhaustive Python and C++ APIs and many other production-oriented features.

https://appleseedhq.net/

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POV-Ray, is the oldest free and open-source 3D renderer. It generates images from a text-based scene description language. It supports mathematically defined primitives as well as their polygonal counterparts; A Turing-complete scene description language (SDL) that supports macros and loops; Subsurface Scattering (sss) and translucency; Atmospheric effects such as fog and media (smoke, clouds); photon mapping; Pause and restart a render after shutdown; Real Time Rendering mode, etc.

Read more in Blender’s exporter wiki.