Limit pitch based on edge insets. Fix max Z calculation in getProjMat…

…rix.

As we don't want to show horizon, there is a need to limit max pitch based on edge insets.
The limit shouldn't be that bad, as to e.g. have 60 deg pitch, top - bottom insets should be less than 0.732 of screen height.

TransformState::getProjMatrix calculation of farZ was an aproximation. Replacing it with simpler, but precise calculation.

Related to: #15163

include/mbgl/util/projection.hpp

@@ -98,7 +98,7 @@ class Projection {
  return Point<double> {
  util::LONGITUDE_MAX + latLng.longitude(),
  util::LONGITUDE_MAX - util::RAD2DEG * std::log(std::tan(M_PI / 4 + latitude * M_PI / util::DEGREES_MAX))
- } * worldSize / util::DEGREES_MAX;
+ } * (worldSize / util::DEGREES_MAX);
  }
 };
 

src/mbgl/map/transform.cpp

@@ -138,9 +138,6 @@ void Transform::easeTo(const CameraOptions& camera, const AnimationOptions& anim
  if (bearing != startBearing) {
  state.bearing = util::wrap(util::interpolate(startBearing, bearing, t), -M_PI, M_PI);
  }
- if (pitch != startPitch) {
- state.pitch = util::interpolate(startPitch, pitch, t);
- }
  if (padding != startEdgeInsets) {
  // Interpolate edge insets
  state.edgeInsets = {
@@ -150,6 +147,10 @@ void Transform::easeTo(const CameraOptions& camera, const AnimationOptions& anim
  util::interpolate(startEdgeInsets.right(), padding.right(), t)
  };
  }
+ auto maxPitch = getMaxPitchForEdgeInsets(state.edgeInsets);
+ if (pitch != startPitch || maxPitch < startPitch) {
+ state.pitch = std::min(maxPitch, util::interpolate(startPitch, pitch, t));
+ }
  }, duration);
 }
 
@@ -302,9 +303,6 @@ void Transform::flyTo(const CameraOptions &camera, const AnimationOptions &anima
  if (bearing != startBearing) {
  state.bearing = util::wrap(util::interpolate(startBearing, bearing, k), -M_PI, M_PI);
  }
- if (pitch != startPitch) {
- state.pitch = util::interpolate(startPitch, pitch, k);
- }
  if (padding != startEdgeInsets) {
  // Interpolate edge insets
  state.edgeInsets = {
@@ -314,6 +312,10 @@ void Transform::flyTo(const CameraOptions &camera, const AnimationOptions &anima
  util::interpolate(startEdgeInsets.right(), padding.right(), us)
  };
  }
+ auto maxPitch = getMaxPitchForEdgeInsets(state.edgeInsets);
+ if (pitch != startPitch || maxPitch < startPitch) {
+ state.pitch = std::min(maxPitch, util::interpolate(startPitch, pitch, k));
+ }
  }, duration);
 }
 
@@ -576,4 +578,14 @@ LatLng Transform::screenCoordinateToLatLng(const ScreenCoordinate& point, LatLng
  return state.screenCoordinateToLatLng(flippedPoint, wrapMode);
 }
 
+double Transform::getMaxPitchForEdgeInsets(const EdgeInsets &insets) const
+{
+ double centerOffsetY = 0.5 * (insets.top() - insets.bottom()); // See TransformState::getCenterOffset.
+
+ const auto height = state.size.height;
+ // See TransformState::fov description: fov = 2 * arctan((height / 2) / (height * 1.5)).
+ const double fovAboveCenter = std::atan((height * 0.5 + centerOffsetY) / (height * 1.5));
+ return M_PI * 0.5 - fovAboveCenter - 0.001; // 0.001 prevents parallel ground to viewport clipping plane.
+}
+
 } // namespace mbgl

src/mbgl/map/transform.hpp

@@ -115,6 +115,10 @@ class Transform : private util::noncopyable {
  std::function<void(double)>,
  const Duration&);
 
+ // We don't want to show horizon: limit max pitch based on edge insets.
+ // e.g. for 60 deg pitch, top - bottom insets should be less than 0.732 of screen height.
+ double getMaxPitchForEdgeInsets(const EdgeInsets &insets) const;
+
  TimePoint transitionStart;
  Duration transitionDuration;
  std::function<bool(const TimePoint)> transitionFrameFn;

src/mbgl/map/transform_state.cpp

@@ -41,13 +41,12 @@ void TransformState::getProjMatrix(mat4& projMatrix, uint16_t nearZ, bool aligne
  // [width/2 + offset.x, 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 fovAboveCenter = getFieldOfView() * (0.5 + offset.y / size.height);
- const double groundAngle = M_PI / 2.0 + getPitch();
- const double aboveCenterSurfaceDistance = std::sin(fovAboveCenter) * cameraToCenterDistance / std::sin(M_PI - groundAngle - fovAboveCenter);
-
-
+ // See TransformState::fov description: fov = 2 * arctan((height / 2) / (height * 1.5)).
+ const double tanFovAboveCenter = (size.height * 0.5 + offset.y) / (size.height * 1.5);
+ const double tanMultiple = tanFovAboveCenter * std::tan(getPitch());
+ assert(tanMultiple < 1);
  // Calculate z distance of the farthest fragment that should be rendered.
- const double furthestDistance = std::cos(M_PI / 2 - getPitch()) * aboveCenterSurfaceDistance + cameraToCenterDistance;
+ const double furthestDistance = cameraToCenterDistance / (1 - tanMultiple);
  // Add a bit extra to avoid precision problems when a fragment's distance is exactly `furthestDistance`
  const double farZ = furthestDistance * 1.01;
 
@@ -64,7 +63,7 @@ void TransformState::getProjMatrix(mat4& projMatrix, uint16_t nearZ, bool aligne
  const bool flippedY = viewportMode == ViewportMode::FlippedY;
  matrix::scale(projMatrix, projMatrix, 1.0, flippedY ? 1 : -1, 1);
 
- matrix::translate(projMatrix, projMatrix, 0, 0, -getCameraToCenterDistance());
+ matrix::translate(projMatrix, projMatrix, 0, 0, -cameraToCenterDistance);
 
  using NO = NorthOrientation;
  switch (getNorthOrientation()) {