博客园_len3d

One Way to Suspend Another Thread In Linux

2012-02-10T16:08:00Z

// at process start call init_pthread_suspending to install the handlers
// to suspend a thread use pthread_kill(thread_id, SUSPEND_SIG)
// to resume a thread use pthread_kill(thread_id, RESUME_SIG)

#include <signal.h>

#define RESUME_SIG SIGUSR2
#define SUSPEND_SIG SIGUSR1

static sigset_t wait_mask;
static __thread int suspended; // per-thread flag

void resume_handler(int sig)
{
    suspended = 0;
}

void suspend_handler(int sig)
{
    if (suspended) return;
    suspended = 1;
    do sigsuspend(&wait_mask); while (suspended);
}

void init_pthread_suspending()
{
    struct sigaction sa;

    sigfillset(&wait_mask);
    sigdelset(&wait_mask, SUSPEND_SIG)
    sigdelset(&wait_mask, RESUME_SIG);

    sigfillset(&sa.sa_mask);
    sa.sa_flags = 0;
    sa.sa_handler = resume_handler;
    sigaction(RESUME_SIG, &sa, NULL);

    sa.sa_handler = suspend_handler;
    sigaction(SUSPEND_SIG, &sa, NULL);
}

本文链接

在Windows 7 64-bit上安装Visual Studio 2008失败的解决方案

2011-10-18T05:20:00Z

错误提示是：

Runtime Pre-requisites: [2] Error: Installation failed for component Runtime Pre-requisites. MSI returned error code 1603

1. 如果你的机器上有.NET Framework 4.0 Extended和.NET Framework 4.0 Client Profile，卸载它们。

2. 重启电脑，这步是必需的。

3. 使用Run as Administrator方式运行Visual Studio 2008的setup.exe。

这样应该就能成功安装了。

本文链接

How to compute dPdu, dPdv for triangles

2011-09-09T06:46:00Z

For triangles, as well as other planar shapes, there's an affine mapping from parametric space to object space, said M.

In parametric space, we know the parametric coordiantes for 3 triangle corners are (u0, v0), (u1, v1), (u2, v2) respectively.

While in object space, the 3D coordinates for 3 triangle corners are P0, P1, P2.

So with the mapping M, we can transform the difference vectors (du1, dv1) = (u1 - u0, v1 - v0), and (du2, dv2) = (u2 - u0, v2 - v0) to the difference vectors in object space, said dP1 = P1 - P0, dP2 = P2 - P0, dP1, dP2 are 3D vectors.

The equation looks like:

(dP1) (du1 dv1)

| | = | | * M

(dP2) (du2 dv2)

Assume M = (K1, K2), K1, K2 are 3D vectors, the equation can be rewritten with:

(dP1) (du1 dv1) (K1)

| | = | | * | | (1)

(dP2) (du2 dv2) (K2)

Solve K1, K2, we get:

(K1) (du1 dv1) (dP1)

| | = INV| | * | |

(K2) (du2 dv2) (dP2)

Now we need to understand what are K1, K2, using equation (1) we have:

dPdu * du = (du 0) * (K1) = K1 * du, thus we know dPdu = K1

(K2)

Similarly,

dPdv * dv = (0 dv) * (K1) = K1 * dv, thus we know dPdv = K2

(K2)

Finally we got:

(dPdu) (du1 dv1) (dP1)

| | = INV| | * | |

(dPdv) (du2 dv2) (dP2)

Which satisfies:

P(u + du, v) = P(u, v) + dPdu * du

P(u, v + dv) = P(u, v) + dPdv * dv

本文链接

More ideas on kd-tree construction

2011-07-26T06:26:00Z

1. Processing each l-th primitive at the binning step, where

l=log10(N) and N is number of primitives in the current node.
2. Experiments demonstrated that it is beneficial to switch to

exact SAH computation when the number of primitives in the current

node is less or equal to the number of bins.
3. Experiments show that using the same fixed number of 32 bins at

any level is sufficient.
4. Re-binning with 32 * 2^N, N is the tree depth.

本文链接

How to use Intel C++ Compiler in Visual Studio 2008

2011-07-15T10:02:00Z

Here are some tips:

1. Convert all VC projects to ICL projects by Use Intel C++.

2. Set Structure Alignment to 1 byte or 4 byte, otherwise ICL may default to 16 byte.

3. If you don't want to have dependency on libmmd.dll, use Multi-threaded rather than Multi-threaded DLL to static link with ICL runtime.

4. It's strongly recommended to build 3ds Max plugin using MSVC, instead of ICL, and you must set Structure Alignment to Default, which 3ds Max always uses(3ds Max is built using MSVC too).

5. ICL may eliminate useful functions which fills global data in current module, but the filled data is only used in other modules, to disable this, I added printf in such functions, nasty fix...

本文链接

Number Prefixes in Mathematics

2011-05-25T03:02:00Z

    Number   Greek        Latin
    ------   -----        -----
       1     mono-        uni-
       2     duo-/di-     duo-/bi-
       3     tri-         tri-
       4     tetra-       quad-
       5     penta-       quint-
       6     hex-         sex-
       7     hept-        sept-
       8     oct-         oct-
       9     ennea-       non-
      10     dec-         dec-
      20     icosa-       vigint-
      30     triaconta-   trigint-
      40     tetraconta- quadragint-
      50     pentaconta- quinquagint-
      60     hexaconta-   sexagint-
      70     heptaconta- septuagint-
      80     octaconta-   octogint-
      90     enneaconta- nonagint-
     100     hect -      cent-

本文链接

数学公式和符号的念法

2011-03-02T07:28:00Z

1 Α α alpha a:lf 阿尔法角度；系数

2 Β β beta bet 贝塔磁通系数；角度；系数

3 Γ γ gamma ga:m 伽马电导系数（小写）

4 Δ δ delta delt 德尔塔变动；密度；屈光度

5 Ε ε epsilon ep`silon 伊普西龙对数之基数

6 Ζ ζ zeta zat 截塔系数；方位角；阻抗；相对粘度；原子序数

7 Η η eta eit 艾塔磁滞系数；效率（小写）

8 Θ θ thet θit 西塔温度；相位角

9 Ι ι iot aiot 约塔微小，一点儿

10 Κ κ kappa kap 卡帕介质常数

11 ∧ λ lambda lambd 兰布达波长（小写）；体积

12 Μ μ mu mju 缪磁导系数；微（千分之一）；放大因数（小写）

13 Ν ν nu nju 纽磁阻系数

14 Ξ ξ xi ksi 克西

15 Ο ο omicron omik`ron 奥密克戎

16 ∏ π pi pai 派圆周率=圆周÷直径=3.1416

17 Ρ ρ rho rou 肉电阻系数（小写）

18 ∑ σ sigma `sigma 西格马总和（大写），表面密度；跨导（小写）

19 Τ τ tau tau 套时间常数

20 Υ υ upsilon jup`silon 宇普西龙位移

21 Φ φ phi fai 佛爱磁通；角

22 Χ χ chi phai 西

23 Ψ ψ psi psai 普西角速；介质电通量（静电力线）；角

24 Ω ω omega o`miga 欧米伽欧姆（大写）；角速（小写）；角

希腊字母读法

Αα：阿尔法 Alpha

Ββ：贝塔 Beta

Γγ：伽玛 Gamma

Δδ：德尔塔 Delte

Εε：艾普西龙 Epsilon

ζ ：捷塔 Zeta

Ζη：依塔 Eta

Θθ：西塔 Theta

Ιι：艾欧塔 Iota

Κκ：喀帕 Kappa

∧λ：拉姆达 Lambda

Μμ：缪 Mu

Νν：拗 Nu

Ξξ：克西 Xi

Οο：欧麦克轮 Omicron

∏π：派 Pi

Ρρ：柔 Rho

∑σ：西格玛 Sigma

Ττ：套 Tau

Υυ：宇普西龙 Upsilon

Φφ：fai Phi

Χχ：器 Chi

Ψψ：普赛 Psi

Ωω：欧米伽 Omega

希腊字母怎么打

打开Office文档之后，在你需要输入希腊字母的时候，先将输入法切换为英文状态，然后同时按下三个键Ctrl+Shift+Q ，工具栏上的“字体”就会发生变化此刻，你再对照下表输入a,b,c……即可得到您想要的希腊字母。注意，大小写状态时所代表的希腊字母也会有大小写区分的哦！

—dash 破折号

‘ ’single quotation marks 单引号

“ ”double quotation marks 双引号

( )parentheses 圆括号

[ ]square brackets 方括号

《》French quotes 法文引号；书名号

...ellipsis 省略号

¨tandem colon 双点号

"ditto 同上

‖parallel 双线号

／virgule 斜线号

＆ampersand = and

～swung dash 代字号

§section; division 分节号

→arrow 箭号；参见号

＋plus 加号；正号

－minus 减号；负号

±plus or minus 正负号

×is multiplied by 乘号

÷is divided by 除号

＝is equal to 等于号

≠is not equal to 不等于号

≡is equivalent to 全等于号

≌is equal to or approximately equal to 等于或约等于号

≈is approximately equal to 约等于号

＜is less than 小于号

＞is more than 大于号

≮is not less than 不小于号

≯is not more than 不大于号

≤is less than or equal to 小于或等于号

≥is more than or equal to 大于或等于号

％per cent 百分之…

‰per mill 千分之…

∞infinity 无限大号

∝varies as 与…成比例

√(square) root 平方根

∵since; because 因为

∴hence 所以

∷equals, as (proportion) 等于，成比例

∠angle 角

⌒semicircle 半圆

⊙circle 圆

○circumference 圆周

πpi 圆周率

△triangle 三角形

⊥perpendicular to 垂直于

∪union of 并，合集

∩intersection of 交，通集

∫the integral of …的积分

∑(sigma) summation of 总和

°degree 度

′minute 分

″second 秒

＃number …号

℃Celsius system 摄氏度

＠at 单价

α( 阿而法)

β( 贝塔)

γ(伽马）

δ（德尔塔）

ε（艾普西龙）

ζ（截塔）

η（艾塔） θ（西塔） ι约塔） κ（卡帕）

λ（兰姆达） μ（米尤） ν（纽） ξ（可系） ο（奥密克戎）

π （派）ρ （若）σ （西格马）τ （套）υ （英文或拉丁字母）

φ（斐） χ（喜） ψ（普西）） ω（欧米伽）

各种符号的英文读法

'exclam'＝'!'

'at'＝'@'

'numbersign'＝'#'

'dollar'＝'$'

'percent'＝'%'

'caret'＝'^'

'ampersand'＝'&'

'asterisk'＝'*'

'parenleft'＝'('

'parenright'＝')'

'minus'＝'-'

'underscore'＝'_'

'equal'＝'='

'plus'＝'+'

'bracketleft'＝'['

'braceleft'＝'{'

'bracketright'＝']'

'braceright'＝'}'

'semicolon'＝';'

'colon'＝':'

'quote'＝'''

'doublequote'＝'"'

'backquote'＝'''

'tilde'＝'~'

'backslash'＝'\'

'bar'＝'|'

'comma'＝','

'less'＝'<'

'period'＝'.'

'greater'＝'>'

'slash'＝'/'

'question'＝'?'

'space'＝' '

~~~~~~~~~~~~~~~~~~~~~~

￣ hyphen 连字符

' apostrophe 省略号；所有格符号

— dash 破折号

‘ ’single quotation marks 单引号

“ ”double quotation marks 双引号

( ) parentheses 圆括号

[ ] square brackets 方括号

Angle bracket

{} Brace

《》French quotes 法文引号；书名号

... ellipsis 省略号

¨ tandem colon 双点号

" ditto 同上

‖ parallel 双线号

／ virgule 斜线号

＆ ampersand = and

～ swung dash 代字号

§ section; division 分节号

→ arrow 箭号；参见号

＋ plus 加号；正号

－ minus 减号；负号

± plus or minus 正负号

× is multiplied by 乘号

÷ is divided by 除号

＝ is equal to 等于号

≠ is not equal to 不等于号

≡ is equivalent to 全等于号

≌ is equal to or approximately equal to 等于或约等于号

≈ is approximately equal to 约等于号

＜ is less than 小于号

＞ is more than 大于号

≮ is not less than 不小于号

≯ is not more than 不大于号

≤ is less than or equal to 小于或等于号

≥ is more than or equal to 大于或等于号

％ per cent 百分之…

‰ per mill 千分之…

∞ infinity 无限大号

∝ varies as 与…成比例

√ (square) root 平方根

∵ since; because 因为

∴ hence 所以

∷ equals, as (proportion) 等于，成比例

∠ angle 角

⌒ semicircle 半圆

⊙ circle 圆

○ circumference 圆周

π pi 圆周率

△ triangle 三角形

⊥ perpendicular to 垂直于

∪ union of 并，合集

∩ intersection of 交，通集

∫ the integral of …的积分

∑ (sigma) summation of 总和

° degree 度

′ minute 分

″ second 秒

＃ number …号

℃ Celsius system 摄氏度

＠ at 单价

x'是x prime(比如转置矩阵)

x"是x double-prime

常用英文数学式/符号的读法

Pronunciation of Numerals 数词的读法

----------------------------------------------------------------------

1.Cardinals and Ordinals 基数和序数

(1)100以内的数词

基数序数

Roman Arabic

Numerals Numerals

罗马数字阿拉伯数字读法数码读法

I 1 one 1st the first

II 2 two 2nd the second

III 3 three 3rd the third

IV 4 four 4th the fourth

V 5 five 5th the fifth

VI 6 six 6th the sixth

VII 7 seven 7th the seventh

VIII 8 eight 8th the eighth

IX 9 nine 9th the ninth

X 10 ten 10th the tenth

XI 11 eleven 11th the eleventh

XII 12 twelve 12th the twelfth

XIII 13 thirteen 13th the thirteenth

XIV 14 fourteen 14th the fourteenth

XV 15 fifteen 15th the fifteenth

XVI 16 sixteen 16th the sixteenth

XVII 17 seventeen 17th the seventeenth

XVIII 18 eighteen 18th the eighteenth

XIX 19 nineteen 19th the nineteenth

XX 20 twenty 20th the twentieth

XXI 21 twenty-one 21st the twenty-first

XXV 25 twenty-five 25th the twenty-fifth

XXX 30 thirty 30th the thirtieth

XL 40 forty 40th the fortieth

L 50 fifty 50th the fiftieth

LX 60 sixty 60th the sixtieth

LXX 70 seventy 70th the seventieth

LXXX 80 eighty 80th the eightieth

XC 90 ninety 90th the ninetieth

IC 99 ninety-nine 99th the ninety-ninth

C 100 one hundred 100th the hundredth

CII 102 a hundred 102nd the (one) hundred

and two and second

246 two hundred and forty-six

751 seven hundred and fifty-one

(2)1000以上的数词

1,000 = one thousand 一千

10,000 = ten thousand 一万

100,000 = one hundred thousand 十万

1,000,000 = one million 一百万

10,000,000 = ten million 一千万

100,000,000=one hundred million 一亿

(3)十亿以上的大数，英美有不同的读法：

英国美国

十亿 one thousand million = one billion

百亿 ten thousand million = ten billion

千亿 one hundred thousand million = one hundred billion

万亿 one billion = one trillion

2.Fractions 分数

通常将分子读为基数，将分母读为序数。

1/2 = a (or one) half

1/3 = a (or one) third

1/4 = a quarter or one fouth

1/5 = a (or one) fifth

2/3 = two thirds

9/10 = nine tenths

53/4 = five and three quarters

15/64= fifteen over (or by) sixty-four

15% = fifteen per cent

4‰ = four per mill

3.Decimals 小数

0.4 = zero (or nought) point four

.01 = point (or decimal) nought one

12.34 = twelve point three four

567.809 = five hundred and sixty-seven point eight nought nine

30.45 = thirty point four five, five recurring

0.3% = decimal three percent

4.Mathematic Forms 数学式

(1) Addition 加法

1+2=3 One and two are three.

2+3=5 Two plus three equals five.

4+0=4 Four and nought is equal to four.

45+70+152=267 45,70 and 152 added are (or make) 267

the sum (or total) is 267.

演算时的读法： Three and seven are ten; I write(or I write down,or I put down)a nought

and carry one. Four and one that I carry are five, and eight make thirteen,and three

sixteen; I write down six and carry one. One and one (that I carry) are two; I put down

two.- The sum (or total, or the result of the addition) is two hundred and sixty. 37,80

and 143 added together, and(or make) 260.

(2)Subtraction 减法

9-4=5 Nine minus four equals (or is equal to) five.

15-7=8 Seven from fifteen leaves eight.

23,654-8,175=15,479 8,175 (take or subtracted) from 23,654 leaves 15,479. The difference

(or The remainder) is 15,479.

Nine from five won`t go.

演算时的读法：Nought from nought (leaves) nought. One from one leaves nought (or nothing).

Two from three (leaves) one. I can`t take (or subtract) five from four; I must borrow ten;

five from fourteen leaves nine.- The difference (or The remainder) is nine thousand one

hundred. 5210 (take or substracted) from 14,310 leaves 9,100.

(3)Multiplication 乘法

1×0=0 One multiplied by nought equals nought.

1×1=1 Once one is one.

2×1=2 Twice one is two.

3×5=15 Three times five is fifteen

6×0=0 Multiply six by nothing, and the result is nothing.

演算时的读法: Five times nine (or Nine multiplied by five) are forty-five; I put down five

and carry four. Five times seven are thirty-five and four (that I carry) are thirty-nine; I write

down nine and carry three. Five times six make thirty and three (that I carry) thirty-three; I put

down thirty-three.

Eight times nine (or Eight nine) are seven two; I write two and carry seven. Eight sevens make

fifty-six and seven are sixty-three. I put down three and carry six. Eight sixes make forty-eight

and six fifty-four; I write down fifty-four.

I now add the partial results (or products) Five. Two and nine are eleven. Three and three are

six and one are seven. Four and three make seven. Five.

(4)Division 除法

9÷3=3 Nine divided by three maks (or is equal to) three.

20÷5=4 Five into twenty goes four times.

4567÷23=198余13 23 into 4567 goes 198 times, and 13 remainder.

The quctient is 198, and 13 remainder.

演算时的读法: Fifteen into thirteen won`t go ; fifteen into one hundred and thirty-eight goes nine

times; nine times fifteen are one hundred and threty-five; one hundred and thirty-five from one hundred

and thirty-eight leaves three; I bring down seven; fifteen into thirty-seven goes twice; twice fifteen

are thirty; thirty from thirty-seven leaves seven.

The (exact) quotient is ninety-two, and seven remainder; 15 into 1387 goes 92 times, and 7 remainder.

5.Time 时间

(1)Hours 钟点

2h.5'8" = two hours five minutes eight seconds 2小时5分8秒

6.18 = six eighteen 6时18分

8.30 a.m.= eight thirty a.m.['ei 'em] 上午8时30分

the 6.05 p.m.train = the six (nought) five p.m.['pi:'em] train 下午6时零5分列车

又二十四小时混合制的写法和读法如下：

0900 = 0 nine hunderd (上午)9时

0910 = 0 nine ten (上午)9时10分

1300 = thirteen hundred 13时(下午1时)

1525 = fifteen twenty-five 15时25分(下午3时25分)

2000 = twenty hundred 20时(下午8时)

at 5 o'c =at five o'clock 五点钟

(2)Date 日期

Oct.1 =October first 10月1日

Oct.1st = October the first 10月1日

Ist Oct. 1949 = teh first of October, nineteen forty-nine 1949年10月1日

3/5 = [英]May (the) third 5月3日；[美]March fifth 3月5日

[附注]联系日期前置词用on.

(3)Year 年份

684 B.C. =Six eighty-four B.C. ['bi:'si:] 公元前684年

1960 = nineteen sixty; nineteen hundred and sixty

19- nineteen something

1950's nineteen fifties 二十世纪五十年代

[附注]联系年份的前置词用in.

6.Numbers 号码

(1)Telephones Numbers　电话号码

1023 = one O two three; ten twenty-three

1227 = one double two (or two two) seven

0386 = O three eight six

0096 = double O(or O O )nine six

7000 = seven O double O = seven thousand

No.26= Number 26 第26号

Room 201 = Room two O one 第201房间

10 Changan Street = Ten Changan Street 长安街10号

(2)Writings 书籍作品

Vol.I = Volume one (or the first volume) 卷一

Chap.II= Chapter two (or the second chapter) 第2章

Page 3 = page Three (or the third page) 第3页

See pp.5-10 = See Pages five to ten 见第5-10页

Act V = Act five (or the fifth act) 第5幕

Hamlet III 1:56 = Hamlet Act Three, Secene One.Line fifty-six 《哈姆雷特》第3幕第一场第56行

Matt.7:12 = Matthew, Chapter Seven, Verse Twelve 《马可福音》第七章第12节

Beethoven Op.49 = Beethoven Opus forty-nine 贝多芬作品第49号

4to = quarto 四本开 8vo = octavo 八本开

(3)Other 其他

World War I = World War One 第一次世界大战

World War II = World War Two 第二次世界大战

Charles I= Charles the First 查理一世

Henry V = Henry the Fifth 亨利五世

Mr.- = Mr. Dash; Mr. So-and-so 某某先生

Mr.B - = Mr. B

-Esq.,of -= the town of Blank Esquire of Blank University 某大学某某先生

the town of = the town of Blank 某某城

The result of the game was 3-0 比赛结果是三比零。

7.Money 货币

(1)British currency 英币

6d. = six pence 六便士

1/2d. = a halfpenny 半便士

11/2d. = a peney halfpenny or three halfpeny or three halfpence一便士半

1/4d. = a farthing 一个铜元

33/4d.= three pence three farghings 三便士三铜元

1s.6d.(or 1/6) = one (shilling) and six (pence) 一先令六便士

￡1.18 = (or￡1.18s.)= one pound eighteen (shillings) 一镑十八先令

￡1.3s.6d. = one pound, three shillings (and) sixpence

4/51/2(or4s.51/2d.) = four (shillings) and five pence halfpenny

(2)U.S. currency

1.20 dollar (and) twenty (cents) 美金一元二角

4.25 = four dollars twenty-five cents 美金四元二角五分

(3)Soviet currency 前苏联币

6 Rb. 15 = six roubles fifteen kopecks 六卢布十五戈比

(4) German currency 德币

1 m. 60 = one mark sixty pfennig -马克六十芬尼

(5)French currency 法国币

1 fr.30 = one franc. thirty (centimes) -法郎三十生丁

0 fr.15 = fifteen centimes 十五生丁

(6) Chinese People's Currency 人民币

1.50 = one yuan and a half 一元五角

JMP 10.35 = JMP ten yuan thirty-five (fen) 人民币十元三角五分

附注：yuan单复数没有变化：也可作为日本本位币“圆”的符号。

8. Weight and Measures 度量衡

(1)length,area, and volume 长度、面积和容积

3 in = three inches 三英寸

15 ft.5 in = fifteen foot five (inches) 十五英尺五英寸

[附注] 尤其在inches省略时, ft.读作foot;如果inches也念出来，ft可以读作fett.

18'6 5/1"= eighteen foot six and a fifth (inches)

10×8feet= ten by eight feet 十英尺长，八英尺宽

5"×4×31/2 = five inches by four by three and a half 长五英寸，宽四英寸，高三英寸半

[附注] 以上二例中，乘号×表示面积或容积。

(2)Weight 重量

12 dr. 23 gr.= Twelve drams twenty-three grains 十二打兰二十三喱

10 oz. 4 dr. = Ten ounces four drams 十盎司打兰

(3)Capacity 容量

3 gi. = three gills 三及耳

1 qt. 1 pt = one quart one pint 一夸脱一品脱

[附注] qt.,pt. 的复数是qts.,pts.,也可以不加s.

20 gal. 5 qt. =Twenty gallons five quarts 二十加仑五夸脱

5 bu. 3 pk. = Five bushels three pecks 五蒲式耳三配克

+　 plus　加号；正号

-　 minus　减号；负号

±　plus or minus　正负号

×　is multiplied by　乘号

÷　is divided by　除号

＝　is equal to　等于号

≠　is not equal to　不等于号

≡　is equivalent to　全等于号

≌　is equal to or approximately equal to　等于或约等于号

≈　is approximately equal to　约等于号

＜　is less than　小于号

＞　is more than　大于号

≮is not less than 不小于号

≯is not more than 不大于号

≤　is less than or equal to　小于或等于号

≥　is more than or equal to　大于或等于号

%　 per cent　百分之…

‰　per mill　千分之…

∞　infinity　无限大号

∝　varies as　与…成比例

√　(square) root　平方根

∵　since; because　因为

∴　hence　所以

∷　equals, as (proportion)　等于，成比例

∠　angle　角

⌒　semicircle　半圆

⊙　circle　圆

○　circumference　圆周

π　pi 圆周率

△　triangle　三角形

⊥　perpendicular to　垂直于

∪　union of　并，合集

∩　intersection of 交，通集

∫　the integral of …的积分

∑　(sigma) summation of　总和

°　degree　度

′　minute　分

″　second　秒

℃　Celsius system　摄氏度

{　open brace, open curly　左花括号

}　close brace, close curly　右花括号

(　open parenthesis, open paren　左圆括号

)　close parenthesis, close paren　右圆括号

() brakets/ parentheses　括号

[　open bracket 左方括号

]　close bracket 右方括号

[] square brackets　方括号

.　period, dot　句号，点

|　vertical bar, vertical virgule　竖线

& amp;　ampersand, and, reference, ref　和，引用

*　asterisk, multiply, star, pointer　星号，乘号，星，指针

/　slash, divide, oblique 斜线，斜杠，除号

//　slash-slash, comment 双斜线，注释符

#　pound　井号

\　backslash, sometimes escape　反斜线转义符，有时表示转义符或续行符

~　tilde　波浪符

.　full stop　句号

,　comma　逗号

:　colon　冒号

;　semicolon　分号

?　question mark　问号

!　exclamation mark (英式英语) exclamation point (美式英语)

'　apostrophe　撇号

-　hyphen　连字号

-- dash 破折号

...　dots/ ellipsis　省略号

"　single quotation marks 单引号

""　double quotation marks 双引号

‖ parallel 双线号

～　swung dash 代字号

§　section; division 分节号

→　arrow 箭号；参见号

本文链接

elvish Template Library Plan

2010-10-30T11:08:00Z

since jedimaster and I decided to rewrite elvish ray(renamed to elvish render) in ANSI C 89, we don't have STL anymore, so, as a substitution, we would like to extend elvish Template Library to support the containers and algorithms below:

containers:

vector

list

slist

queue

map

set

algorithms:

sort

本文链接

Glossy reflections/refractions in large scene

2010-08-30T06:11:00Z

Start rendering...
Running process...
Approximating time: 0 hours 0 minutes 0.014999 seconds.
Running process...
BSP construction time: 0 hours 0 minutes 3.067001 seconds.
Final gathering time: 0 hours 0 minutes 0.000000 seconds.
Running process...
Cleaning process...
Trace time: 0 hours 10 minutes 50.971008 seconds.
Outputing images...
Average BSP Size: 2.559942
Average BSP Depth: 19.347584
Max BSP Size: 20
Max BSP Depth: 27
Num BSP Leaves: 94567
Num BSP Empty Leaves: 7344
Num BSP Nodes: 94566
Num BSP Allocations: 12
Num BSP Extra Bounds: 0
Num BSP Invalid Splits: 0
Num BSP Bad Splits: 61677
BSP Memory Used: 0 MB
GPIT Memory Used: 426 MB
Num GPIT Allocations: 0
Num File Rebuilds: 0
Num Cannot Allocate Bounds: 0
Num Objects: 1
Num Object Instances: 11683
Num Source Primitives: 18225480
Num Tessellated Primitives: 0
Num Temp Allocations: 0
Num Temp Huge Allocations: 0
Num REYES Rays: 0
Num Eye Rays: 3899270
Num Shadow Rays: 10114160
Num Secondary Rays: 15113604
Num Finalgather Rays: 0
Num Probe Rays: 0
Num Photon Rays: 0
Num Asserts: 0
Num Caustic Photons: 0
Num Globillum Photons: 0
Num Stored Caustic Photons: 0
Num Stored Globillum Photons: 0
Num Shot Caustic Photons: 0
Num Shot Globillum Photons: 0
Total Subtree Size: 592.145172 MB
Average Subtree Size: 8.250873 KB
Max Subtree Size: 316.417969 KB
Num Heap Allocations: 0
Database Cache Hit Rate: 100.000000 %
Database Page File Size: 0.000000 MB
Database Compression Rate: 0.000000 %
Database Memory Peak: 607.939148 MB
Database Virtual Memory Peak: 607.939148 MB
Database Data Reads: 0
Database Data Writes: 0
..\..\core\RC_RAY.cpp, Ln 4373, e_RayInterface::intersect uses 0 : 10 : 46.915955, count: 446262216, max dur.: 0.033997
..\..\core\RC_RAY.cpp, Ln 2276, e_RayTessel::access_accel_triangles uses 0 : 7 : 31.765137, count: 1339651837, max dur.: 0.061005
..\..\core\RC_RAY.cpp, Ln 4373, e_RayInterface::intersect uses 0 : 3 : 1.608414, count: 72194990, max dur.: 0.054001
..\..\core\RC_RAY.cpp, Ln 3961, e_RayInterface::generate_ray_subtree uses 0 : 1 : 31.646370, count: 87189, max dur.: 0.031002
..\..\core\RC_RAY.cpp, Ln 4373, e_RayInterface::intersect uses 0 : 1 : 26.564255, count: 32336006, max dur.: 0.080002
d:\elvic\projects\eray\core\include\RC_BSP.h, Ln 657, e_BSPBuilder::classify uses 0 : 1 : 10.257164, count: 393489924, max dur.: 0.009003
..\..\core\RC_RAY.cpp, Ln 4265, e_RayInterface::generate_ray_subtree, build_bsp uses 0 : 1 : 9.327789, count: 73490, max dur.: 0.028999
..\..\core\RC_RAY.cpp, Ln 4018, e_RayInterface::generate_ray_subtree, point_transform uses 0 : 0 : 41.275833, count: 242013, max dur.: 0.006004
d:\elvic\projects\eray\core\include\RC_BSP.h, Ln 414, e_BSPBuilder::FindPlane uses 0 : 0 : 30.605583, count: 9992108, max dur.: 0.003006
..\..\core\RC_RAY.cpp, Ln 4036, e_RayInterface::generate_ray_subtree, translate triangles uses 0 : 0 : 27.799973, count: 242013, max dur.: 0.016998
d:\elvic\projects\eray\core\include\RC_BSP.h, Ln 511, e_BSPBuilder::FindPlane, sort uses 0 : 0 : 21.154747, count: 9992108, max dur.: 0.003006
..\..\core\RC_RAY.cpp, Ln 2235, e_RayTessel::access_triangles uses 0 : 0 : 14.829754, count: 15883236, max dur.: 0.002014
d:\elvic\projects\eray\core\include\RC_BSP.h, Ln 628, e_BSPBuilder::create_leaf uses 0 : 0 : 13.548763, count: 10757161, max dur.: 0.014000
..\..\core\RC_RAY.cpp, Ln 2194, e_RayTessel::access_vertices uses 0 : 0 : 10.692585, count: 15894919, max dur.: 0.002014
d:\elvic\projects\eray\core\include\RC_BSP.h, Ln 256, e_BSPBuilder::FindPlaneFast uses 0 : 0 : 8.679905, count: 1408162, max dur.: 0.007004
..\..\core\RC_RAY.cpp, Ln 2811, e_RayTriangleInstance::create_leaf, create tessel mapping uses 0 : 0 : 5.018021, count: 7162498, max dur.: 0.001999
d:\elvic\projects\eray\core\include\RC_BSP.h, Ln 212, e_BSPBuilder::build_bsp, get all bounds uses 0 : 0 : 4.355999, count: 73490, max dur.: 0.002007
..\..\core\RC_RAY.cpp, Ln 3368, e_RayInterface::begin_tracing, build initial bsp-tree uses 0 : 0 : 3.058998, count: 1, max dur.: 3.058998
d:\elvic\projects\eray\core\include\RC_BSP.h, Ln 212, e_BSPBuilder::build_bsp, get all bounds uses 0 : 0 : 2.549999, count: 1, max dur.: 2.549999
..\..\core\RC_RAY.cpp, Ln 2070, e_RayTessel::get_camera_bound uses 0 : 0 : 2.547001, count: 11683, max dur.: 0.001003
..\..\core\RC_RAY.cpp, Ln 2721, e_RayTriangleInstance::get_bound uses 0 : 0 : 2.475922, count: 23723630, max dur.: 0.003998
..\..\core\RC_RAY.cpp, Ln 4288, e_RayInterface::generate_ray_subtree, copy sub-tree data uses 0 : 0 : 0.875008, count: 73490, max dur.: 0.005997
d:\elvic\projects\eray\core\include\RC_BSP.h, Ln 414, e_BSPBuilder::FindPlane uses 0 : 0 : 0.110004, count: 155089, max dur.: 0.001003
d:\elvic\projects\eray\core\include\RC_BSP.h, Ln 657, e_BSPBuilder::classify uses 0 : 0 : 0.088993, count: 759712, max dur.: 0.001003
d:\elvic\projects\eray\core\include\RC_BSP.h, Ln 511, e_BSPBuilder::FindPlane, sort uses 0 : 0 : 0.058998, count: 155089, max dur.: 0.001003
d:\elvic\projects\eray\core\include\RC_BSP.h, Ln 628, e_BSPBuilder::create_leaf uses 0 : 0 : 0.058014, count: 94567, max dur.: 0.001003
..\..\core\RC_RAY.cpp, Ln 2655, e_RayTesselInstance::create_leaf uses 0 : 0 : 0.048019, count: 87223, max dur.: 0.001003
d:\elvic\projects\eray\core\include\RC_BSP.h, Ln 256, e_BSPBuilder::FindPlaneFast uses 0 : 0 : 0.009998, count: 1154, max dur.: 0.001003
..\..\core\RC_RAY.cpp, Ln 3295, e_RayInterface::begin_tracing, create tessellation instances uses 0 : 0 : 0.006001, count: 1, max dur.: 0.006001
..\..\core\renderer.cpp, Ln 2149, e_Renderer::render, build raytraceable vertices uses 0 : 0 : 0.000999, count: 1, max dur.: 0.000999
d:\elvic\projects\eray\core\include\RC_BSP.h, Ln 720, e_BSPBuilder::classify_no_bound uses 0 : 0 : 0.000000, count: 11683, max dur.: 0.000000
..\..\core\platform.cpp, Ln 1243, _get_osfhandle uses 0 : 0 : 0.000000, count: 0, max dur.: 0.000000
..\..\core\platform.cpp, Ln 1249, CreateFileMapping uses 0 : 0 : 0.000000, count: 0, max dur.: 0.000000
..\..\core\RC_RAY.cpp, Ln 238, generate_ray_accel_triangles uses 0 : 0 : 0.000000, count: 1, max dur.: 0.000000
..\..\core\renderer.cpp, Ln 2170, e_Renderer::render, build raytraceable triangles uses 0 : 0 : 0.000000, count: 1, max dur.: 0.000000
d:\elvic\projects\eray\core\include\RC_BSP.h, Ln 720, e_BSPBuilder::classify_no_bound uses 0 : 0 : 0.000000, count: 10414, max dur.: 0.000000
Cache [0] Memory Limit: 125 MB
       -- Memory Size: 0 MB
       -- Hit Rate: -1.#IND00 %
       -- Purge Fails(Should never happen): 0
       -- Alloc Fails(Should never happen): 0
       -- Num Slots: 0
       -- Rebuild Time: 0 : 0 : 0.000000
Cache [1] Memory Limit: 125 MB
       -- Memory Size: 0 MB
       -- Hit Rate: -1.#IND00 %
       -- Purge Fails(Should never happen): 0
       -- Alloc Fails(Should never happen): 0
       -- Num Slots: 0
       -- Rebuild Time: 0 : 0 : 0.000000
Cache [2] Memory Limit: 125 MB
       -- Memory Size: 0 MB
       -- Hit Rate: -1.#IND00 %
       -- Purge Fails(Should never happen): 0
       -- Alloc Fails(Should never happen): 0
       -- Num Slots: 0
       -- Rebuild Time: 0 : 0 : 0.000000
Cache [3] Memory Limit: 125 MB
       -- Memory Size: 0 MB
       -- Hit Rate: -1.#IND00 %
       -- Purge Fails(Should never happen): 0
       -- Alloc Fails(Should never happen): 0
       -- Num Slots: 0
       -- Rebuild Time: 0 : 0 : 0.000000
Cache [4] Memory Limit: 125 MB
       -- Memory Size: 0 MB
       -- Hit Rate: -1.#IND00 %
       -- Purge Fails(Should never happen): 0
       -- Alloc Fails(Should never happen): 0
       -- Num Slots: 0
       -- Rebuild Time: 0 : 0 : 0.000000
Cache [5] Memory Limit: 125 MB
       -- Memory Size: 0 MB
       -- Hit Rate: -1.#IND00 %
       -- Purge Fails(Should never happen): 0
       -- Alloc Fails(Should never happen): 0
       -- Num Slots: 0
       -- Rebuild Time: 0 : 0 : 0.000000
Cache [6] Memory Limit: 125 MB
       -- Memory Size: 0 MB
       -- Hit Rate: -1.#IND00 %
       -- Purge Fails(Should never happen): 0
       -- Alloc Fails(Should never happen): 0
       -- Num Slots: 0
       -- Rebuild Time: 0 : 0 : 0.000000
Cache [7] Memory Limit: 125 MB
       -- Memory Size: 0 MB
       -- Hit Rate: -1.#IND00 %
       -- Purge Fails(Should never happen): 0
       -- Alloc Fails(Should never happen): 0
       -- Num Slots: 0
       -- Rebuild Time: 0 : 0 : 0.000000
Global BSP average size: 6.425588
Global BSP average depth: 28.085497
Global BSP max size: 216
Global BSP max depth: 17
Global BSP leaves: 10757161
Global BSP empty leaves: 3594663
Global BSP nodes: 10683671
Global BSP memory used: 81 MB
Global BSP bad splits: 716599
BSP indices: 69121084, 263 MB
BSP byte indices: 58916029, 56 MB
BSP ushort indices: 10205055, 19 MB
BSP uint indices: 0, 0 MB
BSP sub-leaf desc: 7162498, 54 MB
BSP primlist desc: 9429540, 107 MB
Completed rendering.
Elapsed time : 0 hours 10 minutes 54.098022 seconds.

本文链接

[Maxim07]中光线与三角形求交算法的推导

2010-07-22T16:25:00Z

"Ray-Triangle Intersection Algorithm for Modern CPU Architectures" Maxim Shevtsov, Alexei Soupikov and Alexander Kapustin (2007) 中的公式推导时的约定与我通常使用的约定不一致，并且叙述并不严格，故自己推导如下：

约定

以下公式均定义在右手系中。

* 表示数乘或点乘（内积），x表示叉乘（外积）

光线（射线）的参数表示为 x = o + d * t (t > 0) (1)

其中x为光线上任意一点，o为光线起点，d为光线方向，t为参数。

三角形的参数表示为 x = (1 - u - v) * p + u * p1 + v * p2 (0 <= u <= 1, 0 <= v <= 1) (2)

x为三角形内的任一点，p, p1, p2为三角形的三个顶点位置，u, v为参数，（1 - u - v, u, v)称为三角形的重心坐标（barycentric coordinates）。

为了方便，令e1 = p1 - p, e2 = p2 - p

我们约定p, p1, p2按顺序构成逆时针的方向为正面，即n = e1 x e2

推导

光线与三角形的交点可以表示为线性方程 (1 - u - v) * p + u * p1 + v * p2 = o + d * t (3)

即 e1 * u + e2 * v - d * t = o - p (4)

设K = -d, L = o - p, 则原式变为 e1 * u + e2 * v + K * t = L (5)

利用Cramer's rule解该线性方程得

t = dett / det, u = detu / det, v = detv / det (6)

其中

det = K * (e1 x e2) = - d * n (7)

dett = L * (e1 x e2) = (o - p) * n (8)

detu = K * (L x e2) = -d * [(o - p) x e2] (9)

detv = K * (e1 x L) = -d * [e1 x (o - p)] (10)

其实到这里，已经求出了判断交点所需的信息，当然基于以上公式，我们还会预计算一些信息，储存在三角形中，减少求交所需的计算量。

事实上，我们可以在公式(6)的分子分母同除以一个数，所得的值不变，利用这一点，我们同除以nw，w是n的最大分量的轴向，令u, v为另外两个轴向，且u < v。

故 det / nw = -(du * nu + dv * nv + dw) (11)

dett / nw = (ou * nu + ov * nv + ow) - (pu * nu + pv * nv + pw) (12)

detu / nw = d * [(p - o) x e2] = d * [p x e2 - o x e2] = du * (pv * e2w - pw * e2v - ov * e2w + ow * e2v) + dv * (pw * e2u - pu * e2w - ow * e2u + ou * e2w) + dw * (pu * e2v - pv * e2u - ou * e2v + ov * e2u) (13)

利用e1 * n = 0, e2 * n = 0我们可以得到

e1w = - (e1u * nu + e1v * nv) (14)

e2w = - (e2u * nu + e2v * nv)

利用公式(11)，我们可以得到

dw = -(du * nu + dv * nv + det / nw) (15)

将公式(14), (15)代入(13)中消去e2w, dw并整理出e2u, e2v得

detu / nw = e2v * [du * (ou - pu) * nu + du * (ov - pv) * nv + dw * (ow - pw) - (pu - ou) * det / nw] - e2u * [dv * (ou - pu) * nu + dv * (ov - pv) * nv + dv * (ow - pw) - (pv - ov) * det / nw] (16)

令Du = du * dett / nw - (pu - ou) * det, Dv = dv * dett / nw - (pv - ov) * det代入(16)得

detu / nw = e2v * Du - e2u * Dv (17)

同理，实际上我们不需要计算，只需要观察公式(9)与公式(10)的区别，把e2换成e1并加一负号得

detv / nw = e1u * Dv - e1v * Du (18)

至此，我们已经推导出了整个算法中需要用到的公式，下节给出算法的代码。

实现

实现中我们为每个三角形预计算并储存如下数据结构，正好是48 Byte大小，可以对齐到16 Byte边界：

struct TriAccel {
    uint w;
    uint nw;
    float np;
    float nu;
    float nv;
    float pu;
    float pv;
    float e1u;
    float e2v;
    float e2u;
    float e1v;
    uint tri_id;
};

预计算三角形代码如下，为了处理背面裁剪增加了一些代码，不多介绍了：

TriAccel::TriAccel(const Vector3f & v1_pos, const Vector3f & v2_pos, const Vector3f & v3_pos)
{
    Vector3f e1;
    Vector3f e2;
    Vector3f n;
    Vector3f absn;
    float maxVal;
    float inv_nw;
    uint u, v;

    sub(e1, v2_pos, v1_pos);
    sub(e2, v3_pos, v1_pos);
    cross(n, e1, e2);
    absn.x = absf(n.x);
    absn.y = absf(n.y);
    absn.z = absf(n.z);

    if (absn.x > absn.y) {
        u = Y_AXIS;
        v = Z_AXIS;
        w = X_AXIS;
        maxVal = absn.x;
    } else {
        u = Z_AXIS;
        v = X_AXIS;
        w = Y_AXIS;
        maxVal = absn.y;
    }
    if (absn.z > maxVal) {
        u = X_AXIS;
        v = Y_AXIS;
        w = Z_AXIS;
    }

    inv_nw = 1.0f / n.arr[w];
    mulvf(n, inv_nw);

    nu = n.arr[u];
    nv = n.arr[v];

    pu = v1_pos.arr[u];
    pv = v1_pos.arr[v];

    np = n.arr[u] * v1_pos.arr[u] + n.arr[v] * v1_pos.arr[v] + v1_pos.arr[w];

    e1u = (e1.arr[u] * inv_nw);
    e1v = (e1.arr[v] * inv_nw);

    e2u = (e2.arr[u] * inv_nw);
    e2v = (e2.arr[v] * inv_nw);

    if (inv_nw >= 0.0f)
    {
        nw = 0x00000000;
    }
    else
    {
        nw = 0x80000000;
    }
}

最后是光线与三角形求交代码：

#define FLOAT_TO_DWORD(x) (*(unsigned long*)(&(x)))

#define FLOAT_BITWISE_XOR(dest, lhs, rhs) \
    FLOAT_TO_DWORD(dest) = (FLOAT_TO_DWORD(lhs)) ^ (FLOAT_TO_DWORD(rhs))

#define FLOAT_BITWISE_OR(dest, lhs, rhs) \
    FLOAT_TO_DWORD(dest) = (FLOAT_TO_DWORD(lhs)) | (FLOAT_TO_DWORD(rhs))

#define FLOAT_MUL_NEGATIVE(lhs, rhs) \
    ((FLOAT_TO_DWORD(lhs) ^ FLOAT_TO_DWORD(rhs)) & 0x80000000) == 0x80000000

static const uint sAxisTable[3][2] = {
    {Y_AXIS, Z_AXIS},
    {Z_AXIS, X_AXIS},
    {X_AXIS, Y_AXIS},
};

bool TriAccel::intersect(const Vector3f & ray_src, const Vector3f & ray_dir, const float t_near, const float t_far, float & t, Vector3f & bary)
{
    float det;
    float dett;
    float Du;
    float Dv;
    float detu;
    float detv;
    float tempdet0;
    float tempdet1;
    uint u, v;

    u = sAxisTable[w][0];
    v = sAxisTable[w][1];

    det = -(ray_dir.arr[u] * nu + ray_dir.arr[v] * nv + ray_dir.arr[w]);

    if (FLOAT_MUL_NEGATIVE(det, nw))
    {
        return false;
    }

    dett = (ray_src.arr[u] * nu + ray_src.arr[v] * nv + ray_src.arr[w]) - np;

    if (FLOAT_MUL_NEGATIVE(det, dett))
    {
        return false;
    }

    Du = ray_dir.arr[u] * dett - (pu - ray_src.arr[u]) * det;
    Dv = ray_dir.arr[v] * dett - (pv - ray_src.arr[v]) * det;
    detu = e2v * Du - e2u * Dv;
    detv = e1u * Dv - e1v * Du;

    tempdet0 = det - detu - detv;

    FLOAT_BITWISE_XOR(tempdet0, tempdet0, detu);
    FLOAT_BITWISE_XOR(tempdet1, detv, detu);
    FLOAT_BITWISE_OR(tempdet0, tempdet0, tempdet1);

    if ((FLOAT_TO_DWORD(tempdet0) & 0x80000000) == 0x80000000)
    {
        return false;
    }

    float inv_det = 1.0f / det;

    t = dett * inv_det;
    if (t > t_far || t < t_near)
    {
        return false;
    }

    bary.y = detu * inv_det;
    bary.z = detv * inv_det;
    bary.x = 1.0f - (bary.y + bary.z);

    return true;
}

到此该睡觉去鸟……文中如有错漏之处，欢迎指正，谢谢！

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