[poincare/zoom] Method ExpandSparseWindow

This method is used to remove extraneous empty sapce in the middle of
the window for functions that are discontinuous between their points of
interest.

poincare/include/poincare/zoom.h

@@ -68,6 +68,10 @@ private:
    * an asymptote, by recursively computing the slopes. In case of an extremum,
    * the slope should taper off toward the center. */
   static bool IsConvexAroundExtremum(ValueAtAbscissa evaluation, float x1, float x2, float x3, float y1, float y2, float y3, Context * context, const void * auxiliary, int iterations = 3);
+  /* If the function is discontinuous between its points of interest, there
+   * might be a lot of empty space in the middle of the screen. In that case,
+   * we want to zoom out to see more of the graph. */
+  static void ExpandSparseWindow(float * sample, int length, float * xMin, float * xMax, float * yMin, float * yMax);
 };
 
 }

poincare/src/zoom.cpp

@@ -201,15 +201,19 @@ void Zoom::RefinedYRangeForDisplay(ValueAtAbscissa evaluation, float * xMin, flo
    * yMax that must be inside the Y range.*/
   assert(yMin && yMax);
 
+  float sample[k_sampleSize];
   float sampleYMin = FLT_MAX, sampleYMax = -FLT_MAX;
   const float step = (*xMax - *xMin) / (k_sampleSize - 1);
   float x, y;
   float sum = 0.f;
   int pop = 0;
 
+  sample[0] = evaluation(*xMin, context, auxiliary);
+  sample[k_sampleSize - 1] = evaluation(*xMax, context, auxiliary);
   for (int i = 1; i < k_sampleSize - 1; i++) {
     x = *xMin + i * step;
     y = evaluation(x, context, auxiliary);
+    sample[i] = y;
     if (!std::isfinite(y)) {
       continue;
     }
@@ -244,6 +248,8 @@ void Zoom::RefinedYRangeForDisplay(ValueAtAbscissa evaluation, float * xMin, flo
   } else if (*yMax < 0.f && *yMax / *yMin < k_forceXAxisThreshold) {
     *yMax = 0.f;
   }
+
+  ExpandSparseWindow(sample, k_sampleSize, xMin, xMax, yMin, yMax);
 }
 
 void Zoom::RangeWithRatioForDisplay(ValueAtAbscissa evaluation, float yxRatio, float * xMin, float * xMax, float * yMin, float * yMax, Context * context, const void * auxiliary) {
@@ -446,4 +452,31 @@ bool Zoom::IsConvexAroundExtremum(ValueAtAbscissa evaluation, float x1, float x2
   return true;
 }
 
+void Zoom::ExpandSparseWindow(float * sample, int length, float * xMin, float * xMax, float * yMin, float * yMax) {
+  /* We compute the "empty center" of the window, i.e. the largest rectangle
+   * (with same center and shape as the window) that does not contain any
+   * point. If that rectangle is deemed too large, we consider that not enough
+   * of the curve shows up on screen and we zoom out. */
+  constexpr float emptyCenterMaxSize = 0.5f;
+  constexpr float ratioCorrection = 4.f/3.f;
+
+  float xCenter = (*xMax + *xMin) / 2.f;
+  float yCenter = (*yMax + *yMin) / 2.f;
+  float xRange = *xMax - *xMin;
+  float yRange = *yMax - *yMin;
+
+  float emptyCenter = FLT_MAX;
+  float step = xRange / (length - 1);
+  for (int i = 0; i < length; i++) {
+    float x = *xMin + i * step;
+    float y = sample[i];
+    float r = 2 * std::max(std::fabs(x - xCenter) / xRange, std::fabs(y - yCenter) / yRange);
+    emptyCenter = std::min(emptyCenter, r);
+  }
+
+  if (emptyCenter > emptyCenterMaxSize) {
+    SetZoom(ratioCorrection + emptyCenter, xCenter, yCenter, xMin, xMax, yMin ,yMax);
+  }
+}
+
 }

poincare/test/zoom.cpp

@@ -128,6 +128,7 @@ QUIZ_CASE(poincare_zoom_refined_range) {
   assert_refined_range_is("x×sin(x)", -14.4815292, 14.4815292, -7.37234354, 7.37234354);
   assert_refined_range_is("x×ln(x)", -0.314885706, 1.36450469, -0.367870897, 0.396377981);
   assert_refined_range_is("x!", -10, 10, NAN, NAN);
+  assert_refined_range_is("xℯ^(1/x)", -1.3, 2.4, -0.564221799, 5.58451653);
 }
 
 void assert_orthonormal_range_is(const char * definition, float targetXMin, float targetXMax, float targetYMin, float targetYMax, Preferences::AngleUnit angleUnit = Radian, const char * symbol = "x") {