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()) {