private static int CalculateBottomY(int x, DirectionVector bottomVector)
{
switch (x)
{
case 0:
return(0);
default:
{
int quotient = (2 * x - 1) * bottomVector.Y / (2 * bottomVector.X);
int remainder = (2 * x - 1) * bottomVector.Y % (2 * bottomVector.X);
return(remainder >= bottomVector.X
? quotient + 1
: quotient);
}
}
}
private static int CalculateTopY(int x, DirectionVector topVector)
{
switch (x)
{
case 0:
return(0);
default:
{
int quotient = (2 * x + 1) * topVector.Y / (2 * topVector.X);
int remainder = (2 * x + 1) * topVector.Y % (2 * topVector.X);
return(remainder > topVector.X
? quotient + 1
: quotient);
}
}
}
// This method has two main purposes: (1) it marks points inside the
// portion that are within the radius as in the field of view, and
// (2) it computes which portions of the following column are in the
// field of view, and puts them on a work queue for later processing.
private static void ComputeFoVForColumnPortion <T>(
int x,
DirectionVector topVector,
DirectionVector bottomVector,
Func <int, int, bool> isOpaque,
Func <int, int, T> setFieldOfView,
decimal radius,
Queue <ColumnPortion> queue)
{
// Search for transitions from opaque to transparent or
// transparent to opaque and use those to determine what
// portions of the *next* column are visible from the origin.
// Start at the top of the column portion and work down.
var topY = CalculateTopY(x, topVector);
// Note that this can find a top cell that is actually entirely blocked by
// the cell below it; consider detecting and eliminating that.
var bottomY = CalculateBottomY(x, bottomVector);
// A more sophisticated algorithm would say that a cell is visible if there is
// *any* straight line segment that passes through *any* portion of the origin cell
// and any portion of the target cell, passing through only transparent cells
// along the way. This is the "Permissive Field Of View" algorithm, and it
// is much harder to implement.
bool?wasLastCellOpaque = null;
for (int y = topY; y >= bottomY; --y)
{
bool inRadius = CheckInRadiusAndSetFieldOfViewAsNeeded(x, y, setFieldOfView, radius);
// A cell that was too far away to be seen is effectively
// an opaque cell; nothing "above" it is going to be visible
// in the next column, so we might as well treat it as
// an opaque cell and not scan the cells that are also too
// far away in the next column.
bool currentIsOpaque = !inRadius || isOpaque(x, y);
if (wasLastCellOpaque != null)
{
if (currentIsOpaque)
{
// We've found a boundary from transparent to opaque. Make a note
// of it and revisit it later.
if (!wasLastCellOpaque.Value)
{
// The new bottom vector touches the upper left corner of
// opaque cell that is below the transparent cell.
queue.Enqueue(new ColumnPortion(
x + 1,
new DirectionVector(x * 2 - 1, y * 2 + 1),
topVector));
}
}
else if (wasLastCellOpaque.Value)
{
// We've found a boundary from opaque to transparent. Adjust the
// top vector so that when we find the next boundary or do
// the bottom cell, we have the right top vector.
//
// The new top vector touches the lower right corner of the
// opaque cell that is above the transparent cell, which is
// the upper right corner of the current transparent cell.
topVector = new DirectionVector(x * 2 + 1, y * 2 + 1);
}
}
wasLastCellOpaque = currentIsOpaque;
}
// Make a note of the lowest opaque-->transparent transition, if there is one.
if (wasLastCellOpaque != null && !wasLastCellOpaque.Value)
{
queue.Enqueue(new ColumnPortion(x + 1, bottomVector, topVector));
}
}