public CRMatrix Compose(CRMatrix b)
{
var result = new CRMatrix();
for (int i = 0; i < 4; i++)
for (int j = 0; j < 4; j++)
{
result.Data[i, j] =
Data[i, 0] * b.Data[0, j] +
Data[i, 1] * b.Data[1, j] +
Data[i, 2] * b.Data[2, j] +
Data[i, 3] * b.Data[3, j];
}
return result;
}
public CRMatrix Compose(CRMatrix b)
{
var result = new CRMatrix();
for (int i = 0; i < 4; i++)
{
for (int j = 0; j < 4; j++)
{
result.Data[i, j] =
Data[i, 0] * b.Data[0, j] +
Data[i, 1] * b.Data[1, j] +
Data[i, 2] * b.Data[2, j] +
Data[i, 3] * b.Data[3, j];
}
}
return(result);
}
private void plotCurve(int channel, int p1, int p2, int p3, int p4)
{
// construct the geometry matrix from the segment
var geometry = new CRMatrix();
for (int i = 0; i < 4; i++)
{
geometry.Data[i, 2] = 0;
geometry.Data[i, 3] = 0;
}
for (int i = 0; i < 2; i++)
{
geometry.Data[0, i] = Points[channel, p1, i];
geometry.Data[1, i] = Points[channel, p2, i];
geometry.Data[2, i] = Points[channel, p3, i];
geometry.Data[3, i] = Points[channel, p4, i];
}
// subdivide the curve 1000 times
// n can be adjusted to give a finer or coarser curve
float d = 1.0f / 1000;
float d2 = d * d;
float d3 = d * d * d;
// construct a temporary matrix for determining the forward differencing deltas
var tmp2 = new CRMatrix();
tmp2.Data[0, 3] = 1;
tmp2.Data[1, 0] = d3;
tmp2.Data[1, 1] = d2;
tmp2.Data[1, 2] = d;
tmp2.Data[2, 0] = 6 * d3;
tmp2.Data[2, 1] = 2 * d2;
tmp2.Data[3, 0] = 6 * d3;
var basis = new CRMatrix(new float[, ] {
{ -0.5f, 1.5f, -1.5f, 0.5f },
{ 1.0f, -2.5f, 2.0f, -0.5f },
{ -0.5f, 0.0f, 0.5f, 0.0f },
{ 0.0f, 1.0f, 0.0f, 0.0f }
});
// compose the basis and geometry matrices
var tmp1 = basis.Compose(geometry);
// compose the above results to get the deltas matrix
var deltas = tmp2.Compose(tmp1);
// extract the x deltas
float x = deltas.Data[0, 0];
float dx = deltas.Data[1, 0];
float dx2 = deltas.Data[2, 0];
float dx3 = deltas.Data[3, 0];
// extract the y deltas
float y = deltas.Data[0, 1];
float dy = deltas.Data[1, 1];
float dy2 = deltas.Data[2, 1];
float dy3 = deltas.Data[3, 1];
int lastx = Math.Max(0, Math.Min(255, (int)Math.Round(x)));
int lasty = Math.Max(0, Math.Min(255, (int)Math.Round(y)));
Data[channel, lastx] = lasty;
// loop over the curve
for (int i = 0; i < 1000; i++)
{
// increment the x values
x += dx;
dx += dx2;
dx2 += dx3;
// increment the y values
y += dy;
dy += dy2;
dy2 += dy3;
int newx = Math.Max(0, Math.Min(255, (int)Math.Round(x)));
int newy = Math.Max(0, Math.Min(255, (int)Math.Round(y)));
// if this point is different than the last one...then draw it
if ((lastx != newx) || (lasty != newy))
{
Data[channel, newx] = newy;
}
lastx = newx;
lasty = newy;
}
}
private void plotCurve(int channel, int p1, int p2, int p3, int p4)
{
// construct the geometry matrix from the segment
var geometry = new CRMatrix();
for (int i = 0; i < 4; i++)
{
geometry.Data[i, 2] = 0;
geometry.Data[i, 3] = 0;
}
for (int i = 0; i < 2; i++)
{
geometry.Data[0, i] = Points[channel, p1, i];
geometry.Data[1, i] = Points[channel, p2, i];
geometry.Data[2, i] = Points[channel, p3, i];
geometry.Data[3, i] = Points[channel, p4, i];
}
// subdivide the curve 1000 times
// n can be adjusted to give a finer or coarser curve
float d = 1.0f / 1000;
float d2 = d * d;
float d3 = d * d * d;
// construct a temporary matrix for determining the forward differencing deltas
var tmp2 = new CRMatrix();
tmp2.Data[0, 3] = 1;
tmp2.Data[1, 0] = d3;
tmp2.Data[1, 1] = d2;
tmp2.Data[1, 2] = d;
tmp2.Data[2, 0] = 6 * d3;
tmp2.Data[2, 1] = 2 * d2;
tmp2.Data[3, 0] = 6 * d3;
var basis = new CRMatrix(new float[,] {
{ -0.5f, 1.5f, -1.5f, 0.5f },
{ 1.0f, -2.5f, 2.0f, -0.5f },
{ -0.5f, 0.0f, 0.5f, 0.0f },
{ 0.0f, 1.0f, 0.0f, 0.0f }
});
// compose the basis and geometry matrices
var tmp1 = basis.Compose(geometry);
// compose the above results to get the deltas matrix
var deltas = tmp2.Compose(tmp1);
// extract the x deltas
float x = deltas.Data[0, 0];
float dx = deltas.Data[1, 0];
float dx2 = deltas.Data[2, 0];
float dx3 = deltas.Data[3, 0];
// extract the y deltas
float y = deltas.Data[0, 1];
float dy = deltas.Data[1, 1];
float dy2 = deltas.Data[2, 1];
float dy3 = deltas.Data[3, 1];
int lastx = Math.Max(0, Math.Min(255, (int)Math.Round(x)));
int lasty = Math.Max(0, Math.Min(255, (int)Math.Round(y)));
Data[channel, lastx] = lasty;
// loop over the curve
for (int i = 0; i < 1000; i++)
{
// increment the x values
x += dx;
dx += dx2;
dx2 += dx3;
// increment the y values
y += dy;
dy += dy2;
dy2 += dy3;
int newx = Math.Max(0, Math.Min(255, (int)Math.Round(x)));
int newy = Math.Max(0, Math.Min(255, (int)Math.Round(y)));
// if this point is different than the last one...then draw it
if ((lastx != newx) || (lasty != newy))
{
Data[channel, newx] = newy;
}
lastx = newx;
lasty = newy;
}
}