computer graphics & visualization reflections. computer graphics & visualization image...

computer graphics & visualization

Image Synthesis

Reflections


Image Synthesis – WS 07/08Dr. Jens Krüger – Computer Graphics and Visualization Group

Planar reflections• Reflect the scene about a planar mirror

– Environment maps won‘t work in general

• Two basic algorithms– 1) flip scene through the mirror and re-render– 2) flip point of view through the mirror and re-render



Planar reflections• Reflect scene through the mirror plane

– Need to find reflection matrix

• Re-render reflected scene– Restrict drawing to the mirrors visible part

Mirror

Reflected scene

Wall



Planar reflections• The reflection matrix

– p[3]: point on plane– n[3]: plane normal– d: n·p

1000

]2[2]2[]2[21]1[]2[2]0[]2[2

]1[2]2[]1[2]1[]1[21]0[]1[2

]0[2]2[]0[2]1[]0[2]0[]0[21

ndnnnnnn

ndnnnnnn

ndnnnnnn



Planar reflections• Algorithm

A) Initialize ModelView matrixB) Multiply ModelView matrix with reflection matrix

- Flips the scene

C) Render scene !!!D) Render mirror plane

• Sets depth values correctly• Don‘t draw color buffer

E) Pull ModelView matrixF) Render unreflected scene



Planar reflections• Problems

– Mirror is not infinite– Reflected scene should not be seen through walls

• Solution– Use stencil buffer to restrict drawing of reflected

scene– Render mirror polygons and set stencil bit– Restrict drawing of restricted scene to stenciled

pixels



Planar reflections• Algorithm

A) Draw scene without mirrors • glEnable(GL_DEPTH_BUFFER_BIT)

B)Draw mirror• glColorMask(0,0,0,0)• glStencilOp(GL_KEEP, GL_KEEP, GL_REPLACE)• glStencilFunc(GL_ALWAYS, 1, ~0)

C)Draw mirror again to reset depth in mirror projection- glDepthRange(1,1)- glDepthFunc(GL_ALWAYS)- glStencilOp(GL_KEEP, GL_KEEP, GL_KEEP)- glStencilFunc(GL_EQUAL, 1, ~0)



Planar reflectionsAlgorithm cont.

D) Draw reflected scene (clip everything in front of the mirror using glClipPlane(…) )

• glDepthRange(0,1)• glDepthFunc(GL_LESS)• glColorMask(1,1,1,1)

E)Draw mirror again to reset stencil and depth values- glColorMask(0,0,0,0)- glStencilOp(GL_KEEP, GL_KEEP, GL_ZERO)- glDepthFunc(GL_ALWAYS)

Repeat for all other mirrors



Planar reflectionsRecursive reflections

– Reflect scene recursively through reflected mirrors• Generate reflection matrix for reflected mirrors

– Successively increment stencil bit in recursive reflections

• Masking within previous masks



Planar reflections• Reflections using texture mapping

– Stores image of reflected environment– Generated by flipping scene or view point through

mirror • Image is mapped onto the reflector

• Rendering from reflected view point

• E‘ = E+2d(-N)

• R‘ = 2(NE)N-EE: view point

N: normal of mirror plane

d: dist of E to mirror plane



Non-Planar Reflections



Environment maps• Used to simulate reflections of the surrounding

scene in an object• Easily realized in software by tracing ´secondary

rays´• Alternative approach:

– Image of the 3D reflected scene is stored in a 2D environment (texture) map

– Secondary rays are looked up in the environment map during rendering



Environment maps



Environment maps• Cube maps

– Capture reflected scene in 6 projected faces




– General layout

– Generated by rendering the scene as seen from the objects center through each face

XNeg ZPos

YPos

YNeg

XPos ZNeg



Environment maps• Cube map example




– Introduce anisotropic sampling• Larger solid angles are subtended near the edges

– View independent• Update only when surrounding scene changes

– Texture coordinate calculation easy to do• Access via 3D texture coordinates, i.e. the reflection vector• Select largest component of reflection vector

– Selects cube face

• Divide other components through– Selects 2D texture coordinate



Environment maps / fixed function• Cube maps hardware support

– OpenGL support for cube maps• glTexImage2D(GL_CUBE_MAP_ENUM, ......)• GL_CUBE_MAP_ENUM one of GL_TEXTURE_CUBE_MAP_POSITIVE(NEGATIVE)_X(Y,Z)• glEnable(GL_TEXTURE_CUBE_MAP)

– Hardware suported calculation of the reflection vector

• reflection_vector

– New automatic texture coordinate generation function

• GL_REFLECTION_MAP• GL_NORMAL_MAP

– Often used to re-normalize directions



Environment maps / fixed functionglActiveTextureARB(GL_TEXTURE0_ARB);glTexEnvi(GL_TEXTURE_ENV,GL_TEXTURE_ENV_MODE,GL_MODULATE);glBindTexture(GL_TEXTURE_2D,g_uiCheesBoardTexture);glEnable(GL_TEXTURE_2D);

// Texture unit #1 contains the cubic environment map with Reflection MappingglActiveTextureARB(GL_TEXTURE1_ARB);glTexEnvi(GL_TEXTURE_ENV,GL_TEXTURE_ENV_MODE,GL_MODULATE);glBindTexture(GL_TEXTURE_CUBE_MAP_ARB,g_uiCubemap);glEnable(GL_TEXTURE_CUBE_MAP_ARB);glTexGeni(GL_S,GL_TEXTURE_GEN_MODE,GL_REFLECTION_MAP_ARB);glTexGeni(GL_T,GL_TEXTURE_GEN_MODE,GL_REFLECTION_MAP_ARB);glTexGeni(GL_R,GL_TEXTURE_GEN_MODE,GL_REFLECTION_MAP_ARB);glEnable(GL_TEXTURE_GEN_S); glEnable(GL_TEXTURE_GEN_T); glEnable(GL_TEXTURE_GEN_R);

// Setup texture matrix to transform world-space reflections back to object-spaceFLOATMATRIX4 invM;invM.getModelview();invM = invM.inverse();invM[12]=0; invM[13]=0; invM[14]=0; glMatrixMode(GL_TEXTURE);glLoadMatrixf(invM.array);glMatrixMode(GL_MODELVIEW);

glCallList(g_iBigSphere);



Environment maps / D3D10 HLSLTextureCube g_txEnvMap;

SamplerState g_samCube{ Filter = ANISOTROPIC; AddressU = Clamp; AddressV = Clamp;};

[..]

float4 PS_EnvMappedScene( VS_OUTPUT_SCENEENV vin ) : SV_Target{ wN = ( mul( vin.Normal, (float3x3)mWorld ) );ac float3 I = vin.wPos.xyz - vEye; float3 wR = I - 2.0f * dot( I, wN ) * wN; float4 CubeSample = lightMul*g_txEnvMap.Sample( g_samCube, wR );

[...]}



Planar reflections + Env MapsCombination of planar mirror reflections and environment maps

– Loop across all reflective objects– Render reflected scene as is– Store result as environment map or planar

reflection map– Repeat loop



Fresnel effects• The Fresnel term defines the ratio of incident

light to reflected light– F = f(,i,material properties)– It specifies the attenuation of light– For some materials like glass or plastic the

attenuation is independent of • Little reflected light at normal angles• Most light is reflected at glancing angles

– For metallic surfaces (high refraction index) the Fresnel term is close to 1



Fresnel effects Transparency with Fresnel term



Fresnel effects• The Fresnel equation (simplified)

– F =

n cosi - t n cosi +t

cosi – n t cosi +n t

+0.5

i: angle of incidence relative to N

n: index of refraction

t: n2+cosi-1 / n

2 2



Fresnel effects• Environment maps with fresnel term

Additive blend of diffuse and Fresnel

weighted mirror term

refraction indices: 1.5, 200

-blending of diffuse and Fresnel

weighted mirror term

refraction indices:1.5, 200



Bump Mapping



Bump mapping• Bumps could be simulated by geometric displacement

– They are detected by relative darkness or lightness of surface features

• Displacement can be avoided by computing the light distribution and by mapping these values onto the surface– Surface details (texture) are interpreted as a heightfield

and its interaction with light is simulated– Bumpmap defines the displacement of details from the

base surface



Bump mapping• Normal pertubation

– Displacement values perturb the surface normal– The lighting at each pixel on the surface is changed

accordingly



Bump mappingSurface displacement

– p´(u,v) = p(u,v) + f(u,v) • N(u,v)

Now the perturbed normal is needed for shading– N´= (Tu x Tv) / |Tu x Tv|

– Tu and Tv are the tangents to the perturbed surface points

– Tu = (px´/u, py

´/u, pz´/u)

– Tv = (px´/v, py

´/v, pz´/v)



Normal mapping



Normal Mapping



Normal Mapping• Similar idea to bump mapping

– Store normals instead of displacements– Avoid difference computation– Requires Tangent Space transformation



Tangent Space• Normals are stored as if the face lies in the x/z

plane and the normal points toward (0,0,1)• During runtime the faces are most likely

oriented differently tangent space transformation



Parallax mapping



Normal vs. Parallax Mapping



Steep Parallax Mapping



Steep Parallax Mapping// tsE = tangent space eye vector

float4 PS(VERTEX2PIXEL input) { const int numSteps = 30; float height = 1.0, step = 1.0 / numSteps;

float2 offset = input.texCoord.xy; float4 NormalBump = txNB.Sample(smLinear, offset); float2 delta = float2(-tsE.x, tsE.y) / (tsE.z * numSteps);

while (NormalBump.a < height) { height -= step; offset += delta; NormalBump = txNB.Sample(smLinear, offset); }

float4 color = txColor.Sample(smLinear, offset); float3 normal = NB.xyz * 2 - 1;

// same for light ray [...]}



Combination of Techniques

computer graphics & visualization reflections. computer graphics & visualization image...

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