Reflections and Shadows on Planar Surfaces

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1 Reflections and Shadows on Planar Surfaces João Madeiras Pereira Animation and 3D Visualisation Course 2010/2011 Reflections - Motivation Not easy to use ray-tracing techniques to simulate real-time reflections By using tricks and functionalities provided by the graphic hardware such effects can be achieved by the pipeline-based rendering

2 Planar reflections Mirror: Ideal reflector planar surface Color calculated by following the reflected ray Alternative: to use reflected geometry through the mirror plane The reflected image of the object is simply the object itself, physically reflected through the mirror plane. Planar reflections Assume plane is y=0 Then apply a mirror scaling matrix: glscalef(1,-1,1); Effect: y

3 Planar reflections Planar reflections How should you render? 1) the ground plan polygon into the stencil buffer 2) the scaled (1,1,-1) model, but mask with stencil buffer 3) the ground plane (semi-transparent) 4) the unscaled model

4 Another example Image courtesy of Kasper Hoey Nielsen Instead of the scale-trick, you can reflect the camera position and direction in the plane Then render reflection image from there Planar Reflections Operations plane y=0: use scale S(1,-1,1) to reflect the geometry and light sources Arbitrary reflector plane: translate to origin and rotate in order to align with y=0, scale; then invert the two initial transforms

5 Reflections OpenGL considerations The reflector has to be partially transparent Setting properly backface culling since mirror scale matrix flips the sense Avoid that reflected geometry can appear at places where there is no reflector geometry. How? Objects that are on the far side (behind) the mirror should not be reflected. How? To set a user-defined clipping plane with the reflector plane equation oriented in the proper sense. Reflexões em Superfícies Planas: Exercício O exercício consiste em implementar um pequeno programa que permita a navegação dentro de uma cena composta por um conjunto de objectos e um chão capaz de reflectir esses mesmos objectos. Ao observarmos o espaço debaixo do chão, não deve de ser possível ver nenhum objecto. Propõem-se as seguintes fases para a realização do algoritmo: Fase 1: Desenhar os objectos reflectidos; limitar o desenho dos objectos reflectidos à superfície de reflexão usando o stencil buffer. Fase 2: Desenhar a superfície de reflexão (o chão neste caso) Fase 3: Desenhar a geometria do Mundo

6 Planar Shadows Provides important visual cues about object placement in the world: - Distances and depth relationships between objects are used by our brain to generate the perception of 3D space Occluders cast shadows onto receivers Study case: receiver is a planar surface Real-Time Planar Shadows Pipeline de visualização tradicional apenas entra em conta com efeitos de reflexão local e não considera oclusões entre uma fonte de luz e objectos que estejam a ser iluminados. Algoritmos como ray-tracing ou radiosidade apresentam soluções elegantes para o cálculo de sombras, mas não podem ser executados em tempo real Técnicas para calcular sombras em tempo real, baseadas no pipeline de visualização tradicional, recorrendo ao hardware actual: Sombras Planares Shadow Volumes Shadow Maps

7 Blinn Technique (1988) Jim Blinn, "Me and My (Fake) Shadow", IEEE Computer Graphics and Applications, January 1988, algorithm where arbitrary objects cast shadows of onto planar surfaces Esta técnica apenas calcula sombras sobre uma única superfície planar previamente escolhida, provenientes de objectos (quaisquer) que se encontrem entre a fonte de luz e a superfície Não considera sombras que os objectos possam projectar uns sobre os outros. Blinn Technique (cont.) Goal: for a point light source, derive the matrix that projects the vertices of an arbitrary object (occluder) on to a ground plane (receiver). Light source is located at l, the vertex to be projected is at v and the projected vertex is at p.

8 Linear Equation (cont.) 2 equations system: parametric line and plane equation Planar Shadow Projection Matrix The linear equation can be converted into a projection matrix M: M should be concatenated with the ModelView matrix

9 Some OpenGL considerations Take measures to avoid allowing the projected objects to be rendered beneath the ground. Why? Safer method: draw the ground plane first, then draw the projected polygons with the z-buffer off, then render the original geometry. Why? Instead of render the shadows with dark color, we could dark the existing color in the color buffer by using blending. How? Use of stencil buffer: 1) to avoid that projected shadows can fall outside of our ground plane 2) to ensure that each pixel is covered at most once (when, why and how?) By darking the existing color, shadows can exhibit specular color. WRONG: projected objets should have no illumination Possible solution: use the stencil buffer to mark all the shadow points on the ground plane, then re-draw the ground with light source turned off: only the ground fragments corresponding to the marked points in the stencill will be shown.