实时阴影渲染技术探索

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"Real Time Shadow——一本关于实时阴影渲染的教科书" 《Real Time Shadow》是由Elmar Eisemann、Michael Schwarz、Ulf Assarsson和Michael Wimmer合著的，由CRC Press（Taylor & Francis Group的子公司）出版的专业书籍。本书深入探讨了实时阴影渲染这一在计算机图形学和游戏开发领域至关重要的主题。出版日期为2011年5月，国际标准书号为978-1-56881-438-4。实时阴影渲染是计算机图形学中的一个核心概念，特别是在现代游戏和虚拟现实应用中，它允许用户在接近即时的反馈下观察场景中的物体如何相互遮挡，从而增强真实感。随着硬件技术的进步，实现实时阴影的技术也不断发展，包括各种各样的阴影映射、VSM（体积阴影贴图）、PCF（百分比最近邻采样）以及更先进的技术如CSM（ Cascaded Shadow Maps）、SSAO（屏幕空间环境光遮蔽）等。书中详细介绍了这些技术的基本原理、优缺点以及实施策略。例如，传统的阴影映射方法虽然简单但可能产生锯齿边缘和分辨率问题；VSM则通过在浮点纹理中存储距离信息来缓解这些问题，但可能会引入噪声；而CSM通过分层处理远近不同的阴影，改善了对近景和远景阴影的处理效果。SSAO是一种间接光照的模拟，可以增加阴影的自然感，但它通常在后处理阶段计算，对性能有较高要求。此外，书中可能还涵盖了阴影质量与性能优化之间的平衡，如何在有限的计算资源下实现最佳视觉效果，以及针对不同硬件平台的优化策略。作者们可能讨论了最新的阴影技术，如基于机器学习的阴影生成方法，这些方法利用深度学习来提高质量和效率。该书的内容不仅适合图形学研究人员，也适用于游戏开发者和对实时图形感兴趣的工程师。通过阅读，读者将能够理解如何在实时环境中有效地实现复杂且逼真的阴影效果，提升交互体验的真实感。总体来说，《Real Time Shadow》是一本全面的教程，旨在帮助读者掌握实时阴影渲染的理论与实践，从而在自己的项目中实现更为生动、真实的视觉效果。书中所包含的信息都是经过验证和高度尊重的来源，尽管作者和出版社已尽力确保数据的准确性，但他们不承担因使用书中信息导致的任何后果。如果有任何未获授权的版权材料，作者和出版社也表达了歉意，并愿意在未来的重印中进行修正。

1.1. Deﬁnition 5

In our articial world, small-scale geometric variations are usually omitted be-

cause, in practice, we cannot aord to work at the scales necessary to capture these

eects. Usually, we tend to represent objects coarsely but rely on specialized shad-

ing functions that encode ne-scale material properties on the surface that other-

wise would be lost. Further, the fact that these functions live on the surface hint

at another very common approximation: we rely on boundary representations (at

least in the case of triangular meshes). Boundary representations are somewhat

similar to ceramic gures, since you usually cannot look beneath the surface and,

hence, there is no way to tell thatthey are hollow. Nonetheless,it is not uncommon

that eects take place underneath the surface that make the object appear dier-

ently; for example, marble and wax show a certain glow because the light is scat-

tered in its interior. To address these phenomena, a great deal of research focuses

on simulating these interactions approximately on the surface. In Appendix C, we

present a quick overview of some of the most common shading models, some of

which even account for the visibility of small-scale details explicitly.

is distinction between shadingand shadows leavesus with an interesting sit-

uation. In the real world,shadows might have all kinds of ambiguities. By contrast,

in our articial universe, details are limited, and shadows are described indepen-

dently of scale and purely in terms of visibility. A denition such as the one given

by Hasenfratz et al. [Hasenfratz03] is mostly sucient—at least as long as only

opaque objects and direct lighting are considered. Completely general real-time

algorithms, going beyond opaque objects and direct-lighting restrictions, remain

a hey challenge, likely to keep computer graphics experts busy for the foreseeable

future.

In order to handle all cases of shadows, we propose a dierent, mathemati-

cally sound shadow denition, which will apply for all algorithms presented in this

book. e experienced reader might want to skip this part and solely take a look at

Figure 1.5 to be familiar with the most important terms, as well as Equations (1.4)

and (1.6), which will be referred to hereaer.

1.1.1 Terminology

In this section, we will introduce the terminology that will be used throughoutthis

book. In order to facilitate understanding, we will avoid a complex mathematical

denition and assume that our scene corresponds to a triangle mesh with per-face

normals. en, the scene geometry, or simply geometry, S is a set of scene points

that form the triangles. Each scene point p has a corresponding normal n

dened

by the underlying triangle.

A light source L is a set of points l forming the light surface. We will refer

to these points as light (source) samples. e light source emits energy into the

Readers familiar with the concepts of manifolds will realize that these denitions easily extend to

such a case.

1.1. Deﬁnition 7

view

frustum

view from

observer

sideview

caster, occluder,

or blocker

receiver

(invisible)

scene points

view

samples

Figure 1.5. A view sample p is the three-dimensional location corresponding to a pixel p

in the rendered view. Occluders/blockers/shadow casters are all elements that obstruct the

light from p.

alently, as a blocker or shadow caster) for p. Objects containing such points in

shadow (i.e., objects onto which a shadow is cast) are called receivers. ere are

situations where receivers and blockers are distinct, or where each receiver is only

shadowed by a subset of occluders. Notably, some algorithms do not allow self-

shadowing (blocker and receiver are the same object).

In practice, we will mostly be interested in computing the shadow for a special

set of receivers, notably the view samples. A view sample is the three-dimensional

point that corresponds to a given pixel of an image. is notion is interesting be-

cause, when we produce an image for a given view, a correctly shadowed rendition

of the scene only needs to compute a correct color for each pixel, not for all points

in the scene.

Figure 1.5 illustrates most of the here-dened terms and can be used as a ref-

erence for the remainder of this book.

1.1.2 The Rendering Equation

So far, we have claried where we can nd shadows. Now, we will discuss their ac-

tual inuence on the appearance of a scene. For this, we need to understand how

light interacts with the surfaces of a scene. Further, we will get to know the corre-

spondingenergeticquantitiesthatallowus to mathematically describethephysical

behavior. While the interactions can be very complex in a physical environment,

perhaps involving quantum mechanics on a microscale and specialized relativity

theory on a larger scale, in most practical scenarios of computer graphics, these

eects can be neglected. Even Maxwell’s equations only play a role in particular

cases of computer graphics. e most prominent and usually visible eects can be

described with a much simpler equation.

Before analyzing the physical model, we will rst introduce the central notion

of light energy: radiance L. It is dened as radiant ux (light energy per unit time;

In this book, we will not consider wavelength dependence, as it is less relevant for shadows.

8 1. Introduction

measured in Watt) per unit solid angle and per unit projected area. e solid an-

gle subtended by an object at a point p is the size of this object projected on the

unit sphere around the point p; in other words, it is a measure of how large an

object appears from p. Intuitively this makes sense because the farther a light is

away, the smaller it will appear and, similarly, the less energy arrives at the loca-

tion. Anyone who ever walked around with a candle in the dark should recognize

this phenomenon. e second observation is that the denition involves per unit

projected area. Physically, it is impossible to have energy be emitted from a single

point; instead, all (real-world)light sources have some actual area, and the emitted

energy is dened in terms of this area.

e main principle is that the outgoing radiance L

leaving a given scene point

p in a certain direction ω is the result of an interaction between the incoming ra-

diance L

(which is the light that arrives on the surface) and the surface properties

(that dene how light is reected, depending on the material). is process is

described by oneofthe fundamental equations in computergraphics, the so-called

rendering equation, introduced by Kajiya [Kajiya86] and Immel et al. [Immel86]:4

(p, ω)=L

(p, ω)+

∫

Ω

(p, ω,

ω)L

(p,

ω)cos(n

ω)d

ω, (1.2)

where n

is the surface normal at p and Ω

denotes the hemisphere above the

surface at p. e equation puts the following functions into a relation:

• L

describes the outgoing radiance as a function of position p and direction

ω. Simply put, it quanties the light (direct and indirect) leaving a point in

a given direction. is term is the one we are interested in for producing an

image (see infobox on page 9).

• L

yields the emitted radiance. Put simply, this is the light produced at a

given point for a given direction. e term is nonzero for light sources.

• L

is the incoming radiance. In principle, this incoming radiance can itself

depend on the outgoing radiance L

ata dierentscene point. issituation

is taken into account in the case of global illumination, where bounced light

is considered; for example, a red surface next to a white wall might reect

some of its red color onto the wall, leading to so-called color bleeding.

• f

is a bidirectional reectance distribution function (BRDF). It describes

how much of the incoming light from direction

ω is reected in direction ω

at a given point p. Note that this function can be very complex, but might

also just be a constant. (More information on this topic can be found in

Appendix C).

4Kajiyaintroducedtheequationin a dierent formulation, butforourexplanationthis simplerform

is more appropriate.

1.1. Deﬁnition 9









Radiance Captured by a Camera

At this point you might wonder, aer all these denitions, how to actually produce an

image even if we had the outgoing radiance L

(p, ω)at disposition. Aer all, L might

be dened in each scene point but is still given per unit area. To understand how this

relates to pixel values, let’s quickly remember how a pinhole camera works, which is the

standard camera used in most real-time applications. ere are more complex models,

but these are out of the scope of this work. For a real-world pinhole camera, light falls

through a pinhole before reaching a receptor. e receptor integrates the incoming

light and transforms it into a pixel color. e receptors themselves have a certain size,

which is exactly how the area quotient disappears in L. Furthermore, light can only

reach a sensor if it passes through the camera’s pinhole. Hence, we need to evaluate

(p, ω)with a direction ω such that the line through p in direction ω passes through

the camera’s pinhole (in DirectX and OpenGL, this corresponds to the camera center).

When precisely evaluating the incoming light on a receptor for a given pixel, one would

need to take the angular variation for dierent points on the receptor into account. In

practice, this is usually neglected and only a single point is evaluated.

e rendering equation is physically based and describes the equilibrium of

energy in a scene. While it is a good model of illumination transport, solving the

equation analytically is dicult (except for a few uninteresting cases). Photore-

alistic rendering aims at nding ecient ways to approximate and populate this

equation. e equation inherently depends upon itself because the outgoing light

at some point might end up being the incoming light for another point. is de-

pendency makes the computation particularly dicult.

Surface-Based Formulation

Employing the notation p →q ∶=

q−p

∥q−p∥

, the following relationship holds:

(p, p →q)=L

(q, q →p)

for a point p that sees q. Along this segment, the energy exchange will not be

hindered by scene geometry. Consequently, the outgoing illumination from one

side is exactly the incoming illumination on the other side and vice versa.

e integration over the directions as denoted in Equation (1.2) can be rein-

terpreted. It corresponds to an integration over a sphere centered at p onto which

all the surrounding geometry is projected as seen from p. We can hence perform

a change of variables and equivalently integrate over the surfaces of the scene S

instead of the directions on a hemisphere, leading to

(p, ω)=L

(p, ω)+

∫

(p, ω,p →q)L

(q, q →p)G(p,q)V(p, q)dq, (1.3)

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