[TA frost wolf \u may- hundred people plan] 2.3 introduction to common functions

2.3HLSL Common functions

2.3.1 Basic mathematical operations

max(a,b) min(a,b) mul(a,b) abs(a) round(x)

sqrt(x) return x The square root of
rsqrt(x) return x The reciprocal of the square root of

degrees(x) Convert radians to angles
redians(x) Convert angles into radians
noise(x) Noise function

2.3.2 Power exponential pair function

pow(x,y) x Of y The next power （x and y Can be an independent variable or a specific number ）
exp(x) Return to e The exponential function at the bottom
exp2(value x) Return to 2 Bottom ,x Is a power of the exponent
ldexp(x,exp) return x And 2 Of exp The product of power
log(x)
log10(x)
log2(x)

frexp(x,out exp) Floating point x Decompose into mantissa and exponent x = ret*2^exp, The return value is the mantissa ,exp The value returned by the parameter is the exponent
（ If x Parameter is 0, Then the mantissa and exponent of this function return 0）

2.3.3 Trigonometric and hyperbolic functions

sin(x) cos(x) tan(x)
sincos(x, out s, out c) return x The sine and cosine of
tan(y,x) asin(x) acos(x) atan(x) atan2(y,x) return y/x The arctangent of
Aforementioned x Values are in radians

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sinh(x) return x The hyperbolic sine of namely (e^x-e^-x) / 2
cosh(x) return x The hyperbolic cosine value of namely (e^x+e^-x) / 2
tanh(x) return x The hyperbolic sine of namely (e^x-e^-x) / (e^x+e^-x)

2.3.4 Data range class

ceil(x) return >=x Minimum integer of
floor(x) return <=x Maximum integer for
step(x,y) x<=y by 1, Otherwise 0
saturate(x) Return to x Clamp to 0 and 1 Between the value of the
clamp(x,min,max) hold x Restriction on [min,max] Within the scope of , Judgment x Is it within this range , If yes, the original value is returned , If not, return to the upper or lower limit
fmod(x,y) return x Yes y Remainder of remainder
frac(x) return x Decimal part of
modf(x, out ip) Will value x Divided into decimal and integral parts ( The symbols of each part are the same as x identical )
ip Returns the integer part , The whole returns the decimal part

The interpolation function

lerp(x,y,s) according to s stay x To y Interpolation between , Return x*(1-s)+y*s;
smoothstep(min,max,x) If x stay [min, max] Within the scope of , Returns a value between 0 And 1 The smoothness between Hermite interpolation , Use smoothstep Create a smooth experience between two values . For example, you can blend two colors smoothly .

2.3.5 Type judgment class

all(x) Determines whether all components of the specified quantity are non-zero , If both are non-zero, return True, otherwise false（ Scalar 、 Vector or matrix can ）
clip(x) If the input value is less than zero , The current pixel is discarded It is often used to determine the range （ It's not just about 0, The return value is void）, Or test alpha, If each component represents the distance to the plane , It can also be used to simulate the shear plane
sign(x) return x It's positive and negative If x Less than zero returns -1, If x Equal to zero returns 0, If x Greater than zero returns 1

isinf(x) Judge whether it is infinite or infinitesimal
isfinite(x) Judge x Whether the parameters are limited
isnan(x) Judge whether it is NAN

2.3.6 Vector and matrix classes

length(v)
normalize(v)
distance(a,b) Express ： Two vectors , Returns the sum of the squares of the differences of the components under the root sign （ No, it is. The distance to the destination ）
dot(a,b) Dot product
cross(a,b) Cross product

determinant(m) Return matrix m The value calculated as a determinant
transpose(m) Return matrix m The transpose matrix of

2.3.7 Ray operation class

reflect(i,n) Return to i Is the incidence direction ,n Is the reflected light in the normal direction
refract(i,n,ri) Return to i Is the incident vector ,n Is the normal direction ,ri Is the refractive index of the refracted light
lit(n_dot_I, n_dot_h, m) They correspond to each other （normallight,normal Half angle vector h, The specular reflection coefficient m） Returns an illumination vector （ The ambient light , Diffuse light , Specular highlights ,1）
faceforward(n,i,ng) The input and output of the surface normal vector facing the view direction is the same element vector , return -n*sign(dot(i,ng))(normal,light,normal)

Illumination vector

Illumination vector （ The ambient light , Diffuse light , Specular highlights ,1）(Blinn Model )

2.3.8 Texture lookup

GPU In slice element processing （PixelShader） The stage is in screen space XY In the coordinate system, each pixel is searched for the corresponding texture element to determine the color of the pixel （ The name is easy to understand ）

1D

Methods are not commonly used , Few store data in this way , Corresponding to a one-dimensional array

2D

Corresponding to two-dimensional array , That's the matrix

3D Texture lookup

Search for 3D data , It is composed of multi-layer two-dimensional arrays .

tex（s,t） In a given texture sampler (s, It refers to the sampled image ) Under the circumstances , adopt t（1D Scalar below ,2D、3D Is vector , That is, the position coordinates ） To determine the texture data .

Projection texture correlation （ Not very clear Look again. ）

tex1Dproj(s, t) Project the texture into the scene as a slide , Firstly, the projection texture coordinates are calculated by using the projection texture technique （ Due to the change of the angle between the projection ray and the projection surface , So the coordinates of the projected texture are not simply scaled , There will also be other problems such as oblique cutting , In addition, the irregular projection surface is also a problem that needs to be solved ）, Finally, we use the projected texture coordinates to query the texture elements .

ddx、ddy Focus on checking by yourself

mipmap

A good picture , Better understand why memory space is only used up 1/3

Stereo texture lookup

Unlike 3D search , You need to specify a specific face , And the performance cost is higher .

summary

Write what you think is most commonly used 5 A function ？

1. When looking at the essentials of the introduction, I found that there are many operations on matrices and vectors , among mul(x,y) As a high-frequency application point, it must be indispensable ;
2. Normalization should also be common , therefore saturate(x) Should also be more commonly used ;
3. The interpolation function ;
4. Ray operation class should be the key and difficult , Generally, objects will be illuminated , It should be a common function ;
5. In texture lookup mipmap Correlation function is an unavoidable problem in the whole rendering process , So it's a common function ;

ddx、ddy and Mipmap

I saw Games101 P9, Begin to understand .

• stay Mipmap in ,ddx and ddy Its main purpose is to calculate the coverage length of screen pixels in the texture , from
  L = MAX(sqrt(ddx(u, v)², ddy(u, v)²)) The approximate side length of the covering texture rectangle can be obtained ;
• recycling D=Log2(L) Get what you need Mipmap The number of layers , take Log2（L） Because ,Mipmap Each layer of is reduced to the upper layer 1/2, Just find Log2（L） layer , here L On this layer is the unit length , Thus, the process of re sampling is saved ;
• also ,Log2（L） In general, it is a non integer , At this time, use the Mipmap Layer to perform another linear interpolation , It can make the result more accurate , therefore Mipmap This method is also called cubic linear interpolation .