实时阴影技术探索

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"实时阴影技术指南" 《实时阴影》是一本全面介绍实时阴影技术理论与实践的专业书籍，由Elmar Eisemann、Michael Schwarz、Ulf Assarsson和Michael Wimmer等专家合著，由CRC Press（Taylor & Francis Group的下属品牌）出版。这本书详细探讨了在计算机图形学和游戏开发领域中实现高效且逼真的实时阴影的各种方法。实时阴影是现代3D图形渲染中的关键元素，对于提升虚拟环境的真实感至关重要。书中的内容可能涵盖了各种实时阴影算法，如阴影贴图、VSM（体素阴影贴图）、PCF（ percentage closer filtering）、PSSM（平行投射阴影贴图）以及更先进的技术，如CSM（ Cascaded Shadow Maps）和VSM改进版，它们能有效地处理远近不同距离的阴影效果，提高阴影质量并减少性能开销。此外，书中可能会讨论阴影的质量与性能之间的平衡，因为在实时环境中，计算效率通常是决定因素。作者可能还会深入到硬件加速、GPU编程（如使用着色器语言如GLSL或HLSL）以及多核心优化等方面，这些都是实现实时阴影计算的关键技术。为了适应不同的应用场景，书里可能还涉及了各种光照模型，如方向光、点光源和聚光灯的阴影处理，以及动态物体和复杂场景下的阴影处理策略。此外，书中或许还会讨论如何处理软阴影、半透明物体的阴影，以及如何减少阴影边缘的锯齿和闪烁现象，以提升视觉效果。《实时阴影》可能还包含了一些实际案例和示例代码，帮助读者理解并应用这些技术到实际项目中。书中可能还提到了一些开源库和工具，如Unity、Unreal Engine等游戏引擎中的阴影实现，以及相关研究论文的引用，为读者提供进一步学习和研究的资源。这本书为读者提供了一个全面了解和掌握实时阴影技术的平台，对于游戏开发者、图形程序员以及对计算机图形学感兴趣的读者来说，是一本宝贵的参考资料。通过阅读本书，读者将能够理解和实施各种高效的实时阴影解决方案，从而在虚拟世界中创造出更加逼真的光影效果。

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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