/// \brief One dimensional midpoint displacement fractal.
///
/// Size must be a power of 2.
/// Falloff is the decay of displacement as the fractal is refined.
/// Array is size + 1 long. array[0] and array[size] are filled
/// with the control points for the fractal.
void Segment::fill1d(BasePoint const & l, BasePoint const &h,
float *array) const
{
array[0] = l.height();
array[m_res] = h.height();
LinInterp li(m_res, l.roughness(), h.roughness());
// seed the RNG.
// The RNG is seeded only once for the line and the seed is based on the
// two endpoints -because they are the common parameters for two adjoining
// tiles
//srand((l.seed() * 1000 + h.seed()));
WFMath::MTRand::uint32 seed[2] = { l.seed(), h.seed() };
WFMath::MTRand rng(seed, 2);
// stride is used to step across the array in a deterministic fashion
// effectively we do the 1/2 point, then the 1/4 points, then the 1/8th
// points etc. this has to be the same order every time because we call
// on the RNG at every point
decltype(getResolution()) stride = m_res / 2;
// depth is used to indicate what level we are on. the displacement is
// reduced each time we traverse the array.
float depth = 1;
while (stride)
{
for (decltype(getResolution()) i = stride; i < m_res; i += stride * 2)
{
auto hh = array[i - stride];
auto lh = array[i + stride];
auto hd = std::fabs(hh - lh);
auto roughness = li.calc(i);
//eliminate the problem where hd is nearly zero, leaving a flat section.
if ((hd * 100.f) < roughness)
{
hd += 0.05f * roughness;
}
array[i] = ((hh + lh) / 2.f) + randHalf(rng) * roughness * hd / (1.f + std::pow(depth, BasePoint::FALLOFF));
}
stride >>= 1;
depth++;
}
}
/// \brief Two dimensional midpoint displacement fractal.
///
/// For a tile where edges are to be filled by 1d fractals.
/// Size must be a power of 2, array is (size + 1) * (size + 1) with the
/// corners the control points.
void Segment::fill2d(const BasePoint& p1, const BasePoint& p2,
const BasePoint& p3, const BasePoint& p4)
{
assert(m_points!=0);
// int line = m_res+1;
// calculate the edges first. This is necessary so that segments tile
// seamlessly note the order in which the edges are calculated and the
// direction. opposite edges are calculated the same way (eg left->right)
// so that the top of one tile matches the bottom of another, likewise
// with sides.
// temporary array used to hold each edge
float * edge = new float[m_size];
// calc top edge and copy into m_points
fill1d(p1,p2,edge);
for (int i=0;i<=m_res;i++) {
m_points[0*m_size + i] = edge[i];
checkMaxMin(edge[i]);
}
// calc left edge and copy into m_points
fill1d(p1,p4,edge);
for (int i=0;i<=m_res;i++) {
m_points[i*m_size + 0] = edge[i];
checkMaxMin(edge[i]);
}
// calc right edge and copy into m_points
fill1d(p2,p3,edge);
for (int i=0;i<=m_res;i++) {
m_points[i*m_size + m_res] = edge[i];
checkMaxMin(edge[i]);
}
// calc bottom edge and copy into m_points
fill1d(p4,p3,edge);
for (int i=0;i<=m_res;i++) {
m_points[m_res*m_size + i] = edge[i];
checkMaxMin(edge[i]);
}
// seed the RNG - this is the 5th and last seeding for the tile.
// it was seeded once for each edge, now once for the tile.
//srand(p1.seed()*20 + p2.seed()*15 + p3.seed()*10 + p4.seed()*5);
WFMath::MTRand::uint32 seed[4]={ p1.seed(), p2.seed(), p3.seed(), p4.seed() };
WFMath::MTRand rng(seed, 4);
QuadInterp qi(m_res, p1.roughness(), p2.roughness(), p3.roughness(), p4.roughness());
float f = BasePoint::FALLOFF;
float depth=0;
// center of m_points is done separately
int stride = m_res/2;
//float roughness = (p1.roughness+p2.roughness+p3.roughness+p4.roughness)/(4.0f);
float roughness = qi.calc(stride, stride);
m_points[stride*m_size + stride] = qRMD(rng, m_points[0 * m_size + stride],
m_points[stride*m_size + 0],
m_points[stride*m_size + m_res],
m_points[m_res*m_size + stride],
roughness,
f, depth);
checkMaxMin(m_points[stride*m_size + stride]);
stride >>= 1;
// skip across the m_points and fill in the points
// alternate cross and plus shapes.
// this is a diamond-square algorithm.
while (stride) {
//Cross shape - + contributes to value at X
//+ . +
//. X .
//+ . +
for (int i=stride;i<m_res;i+=stride*2) {
for (int j=stride;j<m_res;j+=stride*2) {
roughness=qi.calc(i,j);
m_points[j*m_size + i] = qRMD(rng, m_points[(i-stride) + (j+stride) * (m_size)],
m_points[(i+stride) + (j-stride) * (m_size)],
m_points[(i+stride) + (j+stride) * (m_size)],
m_points[(i-stride) + (j-stride) * (m_size)],
roughness, f, depth);
checkMaxMin(m_points[j*m_size + i]);
}
}
depth++;
//Plus shape - + contributes to value at X
//. + .
//+ X +
//. + .
for (int i=stride*2;i<m_res;i+=stride*2) {
for (int j=stride;j<m_res;j+=stride*2) {
roughness=qi.calc(i,j);
m_points[j*m_size + i] = qRMD(rng, m_points[(i-stride) + (j) * (m_size)],
m_points[(i+stride) + (j) * (m_size)],
m_points[(i) + (j+stride) * (m_size)],
m_points[(i) + (j-stride) * (m_size)],
roughness, f , depth);
checkMaxMin(m_points[j*m_size + i]);
}
}
for (int i=stride;i<m_res;i+=stride*2) {
for (int j=stride*2;j<m_res;j+=stride*2) {
roughness=qi.calc(i,j);
m_points[j*m_size + i] = qRMD(rng, m_points[(i-stride) + (j) * (m_size)],
m_points[(i+stride) + (j) * (m_size)],
m_points[(i) + (j+stride) * (m_size)],
m_points[(i) + (j-stride) * (m_size)],
roughness, f, depth);
checkMaxMin(m_points[j*m_size + i]);
}
}
stride>>=1;
depth++;
}
delete [] edge;
}