Download Adding Shadows to Computer Graphics: Projective Shadows and Shadow Maps and more Study notes Computer Graphics in PDF only on Docsity! Adding Shadows to the World Our illumination model does not incorporate shadows • only diffuse, specular, and ambient reflection • we always incorporate contribution of light sources • even if there’s an object in the way How do we get shadows? • more advanced rendering methods – e.g., ray tracing and radiosity • or do some clever things cos cosnL d L s a aI I k I k I kθ φ= + + The Structure of Shadows Point Light Source Occluder or Blocker Shadow Starting with a Restricted Solution Let’s make some simplifying assumptions about the world • the world contains objects + a ground plane • only care about shadows on this ground plane • so we are willing to ignore – shadows of one object on another – self-shadowing by a single object What problem do we need to solve? • given a point and a plane • project an object onto this plane • sounds kind of familiar Projective Shadows The point p lies at the intersection of Substitute ray into plane equation • solve for t • substitute back into ray equation for p This gives us a linear equation for p 0plane: d⋅ + =n u L v p ( ) 0ray and plane t d+ − ⋅ + =L v L n u ( )( ) 0t d⋅ + − + =n L v L ( ) ( ) d L + ⋅ = − − ⋅ − np L v L n v L Projective Shadows We’ve derived a linear equation for a projected shadow point From this, we can derive a corresponding projection matrix • given a point v on the object • compute its projection p on the ground plane • where ( ) ( ) d L + ⋅ = − − ⋅ − np L v L n v L =p Mv x x x y x z x y x y y y z y z x z y z z z x y z d L n L n L n L d L n d L n L n L d L n L n d L n L d n n n ⋅ + − − − − − ⋅ + − − − = − − ⋅ + − − − − − ⋅ n L n L M n L n L Drawing Projective Shadows Requires an extra drawing pass for every light • first, we draw everything the normal way • and for each light, draw every object using shadow projection – load our special transformation – turn off lighting, and draw in a very dark color Need to resolve some practical issues to make sure this works • must make sure shadow is always on top of ground plane – can use glPolygonOffset() for that – or draw plane, then shadow (with Z-buffer off), then world • must make sure shadow doesn’t extend past edges of ground – our transformation projects onto an infinite plane – but the ground may have boundaries – can solve this by using the stencil buffer The OpenGL Stencil Buffer Another buffer, alongside the frame buffer and depth buffer • typically <= 8 bits per pixel • can subject fragments to a stencil test during rasterization – those that fail the test don’t get written to frame buffer • turned on with glEnable(GL_STENCIL_TEST) • test selected with glStencilFunc() • control writing into stencil buffer with glStencilOp() Among other things, can be used to mask drawing operations • fill in the stencil pixels where drawing is allowed (say with 1) • draw scene with glStencilFunc(GL_EQUAL, 1, 1) • fragments where stencil is not 1 are discarded • see Red Book for more details What Points are in Shadow? All points for which rays to/from light source are blocked In other words: all the points that the light can’t see • this sounds like visible surface determination
