Projective Textures & Shadow Mapping...2 What is projective texturing? • An intuition for...

Projective Textures & Shadow Mapping

Prof. Aaron Lanterman School of Electrical and Computer Engineering

Georgia Institute of Technology

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What is projective texturing? • An intuition for projective texturing

– The slide projector analogy

Source: Wolfgang Heidrich [99]

From Stanford CS448A: Real-Time Graphics Architectures lecture 11; see graphics.stanford.edu/courses/cs448a-01-fall

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“Slide projector” - different locations

Images from C. Everitt, “Projective Texture Mapping,” http://www.nvidia.com/object/Projective_Texture_Mapping.html

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Texture matrix

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From “The Cg Tutorial,” p. 252.

ProjectTexture – setup Shader "GPUXX/ProjectTexture" { ! Properties { ! _BaseTex ("Base RGB) Gloss (A)", 2D) = "white" {} ! _ProjTex ("Base RGB)", 2D) = "white" {} ! _SpotPower ("Spotlightiness", Range(0.01,1)) = 0.7! } !!!!uniform sampler2D _BaseTex; !uniform float4 _BaseTex_ST; !uniform sampler2D _ProjTex; !uniform float _SpotPower; !!uniform float4x4 _myProjectorMatrix; !uniform float3 _spotlightDir; !

. . .

ProjectTexture – structures struct a2v { ! float4 v: POSITION; ! float3 n: NORMAL; ! float2 tc: TEXCOORD0; !}; ! !struct v2f { ! float4 sv: SV_POSITION; ! float2 tc: TEXCOORD0; ! float3 vWorldPos: TEXCOORD1; ! float3 nWorld: TEXCOORD2; ! float4 vProjected: TEXCOORD3; !}; !

ProjectTexture – vertex program v2f vert_projecttexture(a2v input) { ! v2f output; ! output.sv = mul(UNITY_MATRIX_MVP, input.v); ! output.vWorldPos = mul(_Object2World, input.v).xyz; ! // To transform normals, we want to use the inverse ! // transpose of upper left 3x3 ! // Putting input.n in first argument is like ! // doing trans((float3x3)_World2Object) * input.n;! output.nWorld = ! normalize(mul(input.n, (float3x3) _World2Object)); ! output.vProjected = mul(_myProjectorMatrix, !

float4(output.vWorldPos,1));! output.tc = TRANSFORM_TEX(input.tc, _BaseTex); ! return output; !} !

ProjectTexture – fragment program float4 frag_projecttexture(v2f input) : COLOR { ! // Only use this shader with a point light ! float3 lightDir = normalize(_WorldSpaceLightPos0.xyz -

input.vWorldPos * _WorldSpaceLightPos0.w); ! float3 eyeDir = !

normalize(_WorldSpaceCameraPos.xyz - input.vWorldPos); ! // Renormalizing because the GPU's interpolator ! // doesn't know this is a unit vector ! float3 n = normalize(input.nWorld); ! float3 diff_almost = !

unity_LightColor0.rgb * max(0, dot(n, lightDir)); ! float spotlightEffect = ! pow(dot(normalize(_spotlightDir), -lightDir),_SpotPower * 128.0); ! diff_almost *= spotlightEffect; ! diff_almost *= tex2Dproj(_ProjTex,input.vProjected); !! float4 base = tex2D(_BaseTex, input.tc); ! float3 output = ! (diff_almost + UNITY_LIGHTMODEL_AMBIENT.rgb) * base.rgb; ! return(float4(output,1)); !} !

C# script to set up projector matrix using UnityEngine; !using System.Collections; !![ExecuteInEditMode] !!public class SetupTextureProjection : MonoBehviour { !

! private Matrix4x4 projectorMatrix; ! private Matrix4x4 offsetMatrix; ! private Camera myCamera; !! void Start () { ! Vector3 halfs = 0.5f * Vector3.one;! offsetMatrix = Matrix4x4.TRS(halfs, Quaternion.identity, halfs); ! myCamera = GetComponent (); ! } !

! void Update () { ! projectorMatrix = offsetMatrix * myCamera.projectionMatrix * !

myCamera.worldToCameraMatrix; ! // Quick & dirty; it would generally be better to set properties ! // in specific materials! Shader.SetGlobalMatrix("_MyProjectorMatrix", projectorMatrix); ! Shader.SetGlobalVector("_spotlightDir", transform.forward); ! } !} !

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Watch out for reverse projection!

Images from C. Everitt, “Projective Texture Mapping,” developer.nvidia.com/object/Projective_Texture_Mapping.html

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Dramatic shadow in 2K Games’ BioShock

From www.wired.com/gaming/gamingreviews/multimedia/2007/08/pl_bioshock?slide=16&slideView=6

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The shadow mapping concept (1)

• Depth testing from the light’s point-of-view – Two pass algorithm

• First, render depth buffer from the light’s point-of-view – The result is a “depth map” or “shadow map” – Essentially a 2D function indicating the depth of

the closest pixels to the light – This depth map is used in the second pass

Slide from C. Everitt, “Shadow Mapping,” Powerpoint presentation, www.nvidia.com/attach/6392

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• Shadow determination with the depth map – Second, render scene from the eye’s point-of-view – For each rasterized fragment

• Determine fragment’s XYZ position relative to the light

• This light position should be setup to match the frustum used to create the depth map

• Compare the depth value at light position XY in the depth map to fragment’s light position Z


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• The Shadow Map Comparison – Two values

• A = Z value from depth map at fragment’s light XY position • B = Z value of fragment’s XYZ light position

–  If B is greater than A, then there must be something closer to the light than the fragment, implies fragment is shadowed

–  If A and B are approximately equal, implies fragment is lit


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Shadow mapping: 2D illustration (1)

light source

eye position

depth map Z = A

fragment's light Z = B

depth map image plane

eye view image plane, a.k.a. the frame buffer

The A < B shadowed fragment case


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light source

eye position

depth map Z = A

fragment's light Z = B

depth map image plane

eye view image plane, a.k.a. the frame buffer

The A ≥ B unshadowed fragment case



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Note image precision mismatch!

The depth map could be at a different resolution from the framebuffer

This mismatch can lead to artifacts



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Visualizing shadow mapping (1) • A fairly complex scene with shadows

the point light source


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• Compare with and without shadows

with shadows without shadows Slide from C. Everitt, “Shadow Mapping,” Powerpoint presentation, www.nvidia.com/attach/6392

Visualizing shadow mapping (2)

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• The scene from the light’s point-of-view

FYI: from the eye's point-of-view again



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• The depth buffer from the light’s point-of-view

FYI: from the light's point-of-view again



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• Projecting the depth map onto the eye’s view

FYI: depth map for light’s point-of-view again



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• Projecting light’s planar distance onto eye’s view



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• Comparing light distance to light depth map

Green is where the light planar

distance and the light depth

map are approximately

equal

Non-green is where shadows should be



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• Scene with shadows

Notice how specular

highlights never appear

in shadows

Notice how curved surfaces cast shadows on each other



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Depth map bias issues

Too little bias, everything begins to shadow

Too much bias, shadow starts too far back

Just right


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Shadow mapping: filtering example GL_NEAREST: blocky GL_LINEAR: antialiased edges

Low shadow map resolution used to heighten filtering artifacts


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Projective texturing with spotlight shadows •  Use a spotlight-style projected texture to give shadow

maps a spotlight falloff


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