[core, ios] replace `altitude` with `fov`

ported from -js: eb6c6596c6a7a61363d30356674e0002153b1d19

`altitude` was a terribly-named variable that was used to indirectly
control the fov. This should eliminate some confusion.

`altitude` was equivalent to `cameraToCenterDistance / height`

6 files changed, 34 insertions, 23 deletions

diff --git a/src/mbgl/map/transform_state.cpp b/src/mbgl/map/transform_state.cpp
index 59ae129518..51ecf52e40 100644
--- a/src/mbgl/map/transform_state.cpp
+++ b/src/mbgl/map/transform_state.cpp
@@ -27,22 +27,24 @@ void TransformState::matrixFor(mat4& matrix, const UnwrappedTileID& tileID) cons
 }
 
 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);
+     // 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 value of the farthest fragment that should be rendered.
+    const double farZ = std::cos(M_PI / 2.0 - getPitch()) * topHalfSurfaceDistance + getCameraToCenterDistance();
 
-    matrix::translate(projMatrix, projMatrix, 0, 0, -getAltitude());
+    matrix::perspective(projMatrix, getFieldOfView(), double(size.width) / size.height, 0.1, farZ);
 
-    // 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));
+    matrix::scale(projMatrix, projMatrix, 1, flippedY ? 1 : -1, 1);
+
+    matrix::translate(projMatrix, projMatrix, 0, 0, -getCameraToCenterDistance());
 
     using NO = NorthOrientation;
     switch (getNorthOrientation()) {
@@ -164,8 +166,12 @@ float TransformState::getAngle() const {
     return angle;
 }
 
-float TransformState::getAltitude() const {
-    return altitude;
+float TransformState::getFieldOfView() const {
+    return fov;
+}
+
+float TransformState::getCameraToCenterDistance() const {
+    return 0.5 * size.height / std::tan(fov / 2.0);
 }
 
 float TransformState::getPitch() const {
diff --git a/src/mbgl/map/transform_state.hpp b/src/mbgl/map/transform_state.hpp
index 6faaf4ac41..a35aa5a255 100644
--- a/src/mbgl/map/transform_state.hpp
+++ b/src/mbgl/map/transform_state.hpp
@@ -56,7 +56,8 @@ public:
 
     // Rotation
     float getAngle() const;
-    float getAltitude() const;
+    float getFieldOfView() const;
+    float getCameraToCenterDistance() const;
     float getPitch() const;
 
     // State
@@ -109,7 +110,11 @@ private:
     double x = 0, y = 0;
     double angle = 0;
     double scale = 1;
-    double altitude = 1.5;
+    // This fov value is somewhat arbitrary. The altitude of the camera used
+    // to be defined as 1.5 screen heights above the ground, which was an
+    // arbitrary choice. This is the fov equivalent to that value calculated with:
+    // `fov = 2 * arctan((height / 2) / (height * 1.5))`
+    double fov = 0.6435011087932844;
     double pitch = 0.0;
 
     // cache values for spherical mercator math
diff --git a/src/mbgl/programs/line_program.cpp b/src/mbgl/programs/line_program.cpp
index 2cadaa6c11..cd53337c10 100644
--- a/src/mbgl/programs/line_program.cpp
+++ b/src/mbgl/programs/line_program.cpp
@@ -25,7 +25,7 @@ Values makeValues(const LinePaintProperties::Evaluated& properties,
 
     // calculate how much longer the real world distance is at the top of the screen
     // than at the middle of the screen.
-    float topedgelength = std::sqrt(std::pow(state.getSize().height, 2.0f) / 4.0f  * (1.0f + std::pow(state.getAltitude(), 2.0f)));
+    float topedgelength = std::sqrt(std::pow(state.getSize().height, 2.0f) / 4.0f  * (1.0f + std::pow(state.getCameraToCenterDistance(), 2.0f)));
     float x = state.getSize().height / 2.0f * std::tan(state.getPitch());
 
     return Values {
diff --git a/src/mbgl/programs/symbol_program.cpp b/src/mbgl/programs/symbol_program.cpp
index 71b45ad4fc..d609dada8d 100644
--- a/src/mbgl/programs/symbol_program.cpp
+++ b/src/mbgl/programs/symbol_program.cpp
@@ -23,8 +23,8 @@ Values makeValues(const style::SymbolPropertyValues& values,
         extrudeScale.fill(tile.id.pixelsToTileUnits(1, state.getZoom()) * scale);
     } else {
         extrudeScale = {{
-            pixelsToGLUnits[0] * scale * state.getAltitude(),
-            pixelsToGLUnits[1] * scale * state.getAltitude()
+            pixelsToGLUnits[0] * scale * state.getCameraToCenterDistance(),
+            pixelsToGLUnits[1] * scale * state.getCameraToCenterDistance()
         }};
     }
 
@@ -77,7 +77,7 @@ static SymbolSDFProgram::UniformValues makeSDFValues(const style::SymbolProperty
     const float gammaBase = 0.105 * values.sdfScale / values.paintSize / pixelRatio;
     const float gammaScale = (values.pitchAlignment == AlignmentType::Map
         ? 1.0 / std::cos(state.getPitch())
-        : 1.0) / state.getAltitude();
+        : 1.0) / state.getCameraToCenterDistance();
 
     return makeValues<SymbolSDFProgram::UniformValues>(
         values,
diff --git a/src/mbgl/renderer/painter_circle.cpp b/src/mbgl/renderer/painter_circle.cpp
index 9385b7b1a3..966d58b59b 100644
--- a/src/mbgl/renderer/painter_circle.cpp
+++ b/src/mbgl/renderer/painter_circle.cpp
@@ -47,8 +47,8 @@ void Painter::renderCircle(PaintParameters& parameters,
             uniforms::u_scale_with_map::Value{ scaleWithMap },
             uniforms::u_extrude_scale::Value{ scaleWithMap
                 ? std::array<float, 2> {{
-                    pixelsToGLUnits[0] * state.getAltitude(),
-                    pixelsToGLUnits[1] * state.getAltitude()
+                    pixelsToGLUnits[0] * state.getCameraToCenterDistance(),
+                    pixelsToGLUnits[1] * state.getCameraToCenterDistance()
                   }}
                 : pixelsToGLUnits }
         },
diff --git a/src/mbgl/style/layers/custom_layer_impl.cpp b/src/mbgl/style/layers/custom_layer_impl.cpp
index 3f11943478..baf55205c4 100644
--- a/src/mbgl/style/layers/custom_layer_impl.cpp
+++ b/src/mbgl/style/layers/custom_layer_impl.cpp
@@ -57,7 +57,7 @@ void CustomLayer::Impl::render(const TransformState& state) const {
     parameters.zoom = state.getZoom();
     parameters.bearing = -state.getAngle() * util::RAD2DEG;
     parameters.pitch = state.getPitch();
-    parameters.altitude = state.getAltitude();
+    parameters.fieldOfView = state.getFieldOfView();
 
     renderFn(context, parameters);
 }