void TransformState::getProjMatrix(mat4& projMatrix) const {
double halfFov = std::atan(0.5 / getAltitude());
double topHalfSurfaceDistance = std::sin(halfFov) * getAltitude() /
std::sin(M_PI / 2.0f - getPitch() - halfFov);
// Calculate z value of the farthest fragment that should be rendered.
double farZ = std::cos(M_PI / 2.0f - getPitch()) * topHalfSurfaceDistance + getAltitude();
matrix::perspective(projMatrix, 2.0f * std::atan((size.height / 2.0f) / getAltitude()),
double(size.width) / size.height, 0.1, farZ);
matrix::translate(projMatrix, projMatrix, 0, 0, -getAltitude());
// After the rotateX, z values are in pixel units. Convert them to
// altitude unites. 1 altitude unit = the screen height.
const bool flippedY = viewportMode == ViewportMode::FlippedY;
matrix::scale(projMatrix, projMatrix, 1, flippedY ? 1 : -1,
1.0f / (rotatedNorth() ? size.width : size.height));
using NO = NorthOrientation;
switch (getNorthOrientation()) {
case NO::Rightwards: matrix::rotate_y(projMatrix, projMatrix, getPitch()); break;
case NO::Downwards: matrix::rotate_x(projMatrix, projMatrix, -getPitch()); break;
case NO::Leftwards: matrix::rotate_y(projMatrix, projMatrix, -getPitch()); break;
default: matrix::rotate_x(projMatrix, projMatrix, getPitch()); break;
}
matrix::rotate_z(projMatrix, projMatrix, getAngle() + getNorthOrientationAngle());
matrix::translate(projMatrix, projMatrix, pixel_x() - size.width / 2.0f,
pixel_y() - size.height / 2.0f, 0);
}
void TransformState::getProjMatrix(mat4& projMatrix, uint16_t nearZ) const {
if (size.isEmpty()) {
return;
}
// Find the distance from the center point [width/2, height/2] to the
// center top point [width/2, 0] in Z units, using the law of sines.
// 1 Z unit is equivalent to 1 horizontal px at the center of the map
// (the distance between[width/2, height/2] and [width/2 + 1, height/2])
const double halfFov = getFieldOfView() / 2.0;
const double groundAngle = M_PI / 2.0 + getPitch();
const double topHalfSurfaceDistance = std::sin(halfFov) * getCameraToCenterDistance() / std::sin(M_PI - groundAngle - halfFov);
// Calculate z distance of the farthest fragment that should be rendered.
const double furthestDistance = std::cos(M_PI / 2 - getPitch()) * topHalfSurfaceDistance + getCameraToCenterDistance();
// Add a bit extra to avoid precision problems when a fragment's distance is exactly `furthestDistance`
const double farZ = furthestDistance * 1.01;
matrix::perspective(projMatrix, getFieldOfView(), double(size.width) / size.height, nearZ, farZ);
const bool flippedY = viewportMode == ViewportMode::FlippedY;
matrix::scale(projMatrix, projMatrix, 1, flippedY ? 1 : -1, 1);
matrix::translate(projMatrix, projMatrix, 0, 0, -getCameraToCenterDistance());
using NO = NorthOrientation;
switch (getNorthOrientation()) {
case NO::Rightwards: matrix::rotate_y(projMatrix, projMatrix, getPitch()); break;
case NO::Downwards: matrix::rotate_x(projMatrix, projMatrix, -getPitch()); break;
case NO::Leftwards: matrix::rotate_y(projMatrix, projMatrix, -getPitch()); break;
default: matrix::rotate_x(projMatrix, projMatrix, getPitch()); break;
}
matrix::rotate_z(projMatrix, projMatrix, getAngle() + getNorthOrientationAngle());
matrix::translate(projMatrix, projMatrix, pixel_x() - size.width / 2.0f,
pixel_y() - size.height / 2.0f, 0);
matrix::scale(projMatrix, projMatrix, 1, 1,
1.0 / Projection::getMetersPerPixelAtLatitude(getLatLng(LatLng::Unwrapped).latitude(), getZoom()));
}
void TransformState::getProjMatrix(mat4& projMatrix, uint16_t nearZ, bool aligned) const {
if (size.isEmpty()) {
return;
}
// Find the distance from the center point [width/2, height/2] to the
// center top point [width/2, 0] in Z units, using the law of sines.
// 1 Z unit is equivalent to 1 horizontal px at the center of the map
// (the distance between[width/2, height/2] and [width/2 + 1, height/2])
const double halfFov = getFieldOfView() / 2.0;
const double groundAngle = M_PI / 2.0 + getPitch();
const double topHalfSurfaceDistance = std::sin(halfFov) * getCameraToCenterDistance() / std::sin(M_PI - groundAngle - halfFov);
// Calculate z distance of the farthest fragment that should be rendered.
const double furthestDistance = std::cos(M_PI / 2 - getPitch()) * topHalfSurfaceDistance + getCameraToCenterDistance();
// Add a bit extra to avoid precision problems when a fragment's distance is exactly `furthestDistance`
const double farZ = furthestDistance * 1.01;
matrix::perspective(projMatrix, getFieldOfView(), double(size.width) / size.height, nearZ, farZ);
const bool flippedY = viewportMode == ViewportMode::FlippedY;
matrix::scale(projMatrix, projMatrix, 1, flippedY ? 1 : -1, 1);
matrix::translate(projMatrix, projMatrix, 0, 0, -getCameraToCenterDistance());
using NO = NorthOrientation;
switch (getNorthOrientation()) {
case NO::Rightwards: matrix::rotate_y(projMatrix, projMatrix, getPitch()); break;
case NO::Downwards: matrix::rotate_x(projMatrix, projMatrix, -getPitch()); break;
case NO::Leftwards: matrix::rotate_y(projMatrix, projMatrix, -getPitch()); break;
default: matrix::rotate_x(projMatrix, projMatrix, getPitch()); break;
}
matrix::rotate_z(projMatrix, projMatrix, getAngle() + getNorthOrientationAngle());
const double dx = pixel_x() - size.width / 2.0f, dy = pixel_y() - size.height / 2.0f;
matrix::translate(projMatrix, projMatrix, dx, dy, 0);
if (axonometric) {
// mat[11] controls perspective
projMatrix[11] = 0;
// mat[8], mat[9] control x-skew, y-skew
projMatrix[8] = xSkew;
projMatrix[9] = ySkew;
}
matrix::scale(projMatrix, projMatrix, 1, 1,
1.0 / Projection::getMetersPerPixelAtLatitude(getLatLng(LatLng::Unwrapped).latitude(), getZoom()));
// Make a second projection matrix that is aligned to a pixel grid for rendering raster tiles.
// We're rounding the (floating point) x/y values to achieve to avoid rendering raster images to fractional
// coordinates. Additionally, we adjust by half a pixel in either direction in case that viewport dimension
// is an odd integer to preserve rendering to the pixel grid. We're rotating this shift based on the angle
// of the transformation so that 0°, 90°, 180°, and 270° rasters are crisp, and adjust the shift so that
// it is always <= 0.5 pixels.
if (aligned) {
const float xShift = float(size.width % 2) / 2, yShift = float(size.height % 2) / 2;
const double angleCos = std::cos(angle), angleSin = std::sin(angle);
double devNull;
const float dxa = -std::modf(dx, &devNull) + angleCos * xShift + angleSin * yShift;
const float dya = -std::modf(dy, &devNull) + angleCos * yShift + angleSin * xShift;
matrix::translate(projMatrix, projMatrix, dxa > 0.5 ? dxa - 1 : dxa, dya > 0.5 ? dya - 1 : dya, 0);
}
}