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Tutorial Effects - Function Printing

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TOC: Of Effects and Shaders
Back: Mr. Wiggle
Next: Vertex Data

There are various possibilities to alter the vertex positions by mathematical functions.

For the following examples we use a Grid (EX9.Geometry) as input. Set the resolution to about 50x50.

f(x, y) = z

Create a new z coordinate by x and y. Using the MrWiggle example we could write:

float2 Frequency = 10;
float2 Phase = 0;
float2 Amplitude = 0.01;
 
vs2ps VS(
    float4 PosO  : POSITION,
    float4 TexCd : TEXCOORD0)
{
    //declare output struct
    vs2ps Out;
 
    //calculate two waves
    float2 wave = sin(PosO.xy * Frequency + Phase) * Amplitude;
 
    //set z coordinate
    PosO.z = wave.x + wave.y;
 
    //transform position
    Out.Pos = mul(PosO, tWVP);
 
    //transform texturecoordinates
    Out.TexCd = mul(TexCd, tTex);
 
    return Out;
}

using a patch like:

f(u, v) = xyz

Another common type is to calculate a completely new position from the xy coordinates of the grid. This is often called parametric surfaces, where the xy input parameters are called uv.

for example a cone:

x = v*cos(u)
y = v*sin(u)
z = v

can be written as a function:

float3 Cone(float2 uv)
{
    float u = uv.x;
    float v = uv.y;
 
    float3 newPos;
    newPos.x = v * cos(u);
    newPos.y = v * sin(u);
    newPos.z = v;
 
    return newPos;
}

It might be handy to scale u by two pi to get a full cycle in the range 0..1, as well as have a general offset and scale for the input parameters. The vertex shader could then look like:

#define twopi 6.28318531
 
float2 Scale = 1;
float2 Offset = 0;
 
float3 Cone(float2 uv)
{
 
     uv *= Scale;
     uv += Offset;
 
    float u = uv.x * twopi;
    float v = uv.y;
 
    float3 newPos;
    newPos.x = v * cos(u);
    newPos.y = v * sin(u);
    newPos.z = v;
 
    return newPos;
}
 
vs2ps VS(
    float4 PosO  : POSITION,
    float4 TexCd : TEXCOORD0)
{
    //declare output struct
    vs2ps Out;
 
    //set new position
    PosO.xyz = Cone(PosO.xy);
 
    //transform position
    Out.Pos = mul(PosO, tWVP);
 
    //transform texturecoordinates
    Out.TexCd = mul(TexCd, tTex);
 
    return Out;
}

And the patch:

Next: Vertex Data
Back: Mr. Wiggle
TOC: Of Effects and Shaders

Tutorial Effects - Function Printing

f(x, y) = z

f(u, v) = xyz

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