cc/base/math_util.h

   1 // Copyright 2012 The Chromium Authors. All rights reserved.
   2 // Use of this source code is governed by a BSD-style license that can be
   3 // found in the LICENSE file.
   4
   5 #ifndef CC_BASE_MATH_UTIL_H_
   6 #define CC_BASE_MATH_UTIL_H_
   7
   8 #include <algorithm>
   9 #include <cmath>
  10 #include <vector>
  11
  12 #include "base/logging.h"
  13 #include "base/memory/scoped_ptr.h"
  14 #include "cc/base/cc_export.h"
  15 #include "ui/gfx/geometry/box_f.h"
  16 #include "ui/gfx/geometry/point3_f.h"
  17 #include "ui/gfx/geometry/point_f.h"
  18 #include "ui/gfx/geometry/scroll_offset.h"
  19 #include "ui/gfx/geometry/size.h"
  20 #include "ui/gfx/transform.h"
  21
  22 namespace base {
  23 class Value;
  24 namespace trace_event {
  25 class TracedValue;
  26 }
  27 }  // namespace base
  28
  29 namespace gfx {
  30 class QuadF;
  31 class Rect;
  32 class RectF;
  33 class Transform;
  34 class Vector2dF;
  35 class Vector2d;
  36 class Vector3dF;
  37 }
  38
  39 namespace cc {
  40
  41 struct HomogeneousCoordinate {
  42   HomogeneousCoordinate(SkMScalar x, SkMScalar y, SkMScalar z, SkMScalar w) {
  43     vec[0] = x;
  44     vec[1] = y;
  45     vec[2] = z;
  46     vec[3] = w;
  47   }
  48
  49   bool ShouldBeClipped() const { return w() <= 0.0; }
  50
  51   gfx::PointF CartesianPoint2d() const {
  52     if (w() == SK_MScalar1)
  53       return gfx::PointF(x(), y());
  54
  55     // For now, because this code is used privately only by MathUtil, it should
  56     // never be called when w == 0, and we do not yet need to handle that case.
  57     DCHECK(w());
  58     SkMScalar inv_w = SK_MScalar1 / w();
  59     return gfx::PointF(x() * inv_w, y() * inv_w);
  60   }
  61
  62   gfx::Point3F CartesianPoint3d() const {
  63     if (w() == SK_MScalar1)
  64       return gfx::Point3F(x(), y(), z());
  65
  66     // For now, because this code is used privately only by MathUtil, it should
  67     // never be called when w == 0, and we do not yet need to handle that case.
  68     DCHECK(w());
  69     SkMScalar inv_w = SK_MScalar1 / w();
  70     return gfx::Point3F(x() * inv_w, y() * inv_w, z() * inv_w);
  71   }
  72
  73   SkMScalar x() const { return vec[0]; }
  74   SkMScalar y() const { return vec[1]; }
  75   SkMScalar z() const { return vec[2]; }
  76   SkMScalar w() const { return vec[3]; }
  77
  78   SkMScalar vec[4];
  79 };
  80
  81 class CC_EXPORT MathUtil {
  82  public:
  83   static const double kPiDouble;
  84   static const float kPiFloat;
  85
  86   static double Deg2Rad(double deg) { return deg * kPiDouble / 180.0; }
  87   static double Rad2Deg(double rad) { return rad * 180.0 / kPiDouble; }
  88
  89   static float Deg2Rad(float deg) { return deg * kPiFloat / 180.0f; }
  90   static float Rad2Deg(float rad) { return rad * 180.0f / kPiFloat; }
  91
  92   static float Round(float f) {
  93     return (f > 0.f) ? std::floor(f + 0.5f) : std::ceil(f - 0.5f);
  94   }
  95   static double Round(double d) {
  96     return (d > 0.0) ? std::floor(d + 0.5) : std::ceil(d - 0.5);
  97   }
  98
  99   // RoundUp rounds up a given |n| to be a multiple of |mul|.
 100   // Examples:
 101   //    - RoundUp(123, 50) returns 150.
 102   //    - RoundUp(-123, 50) returns -100.
 103   template <typename T>
 104   static T RoundUp(T n, T mul) {
 105     static_assert(std::numeric_limits<T>::is_integer,
 106                   "T must be an integer type");
 107     return (n > 0) ? ((n + mul - 1) / mul) * mul : (n / mul) * mul;
 108   }
 109
 110   // RoundDown rounds down a given |n| to be a multiple of |mul|.
 111   // Examples:
 112   //    - RoundDown(123, 50) returns 100.
 113   //    - RoundDown(-123, 50) returns -150.
 114   template <typename T>
 115   static T RoundDown(T n, T mul) {
 116     static_assert(std::numeric_limits<T>::is_integer,
 117                   "T must be an integer type");
 118     return (n > 0) ? (n / mul) * mul : (n == 0) ? 0
 119                                                 : ((n - mul + 1) / mul) * mul;
 120   }
 121
 122   template <typename T> static T ClampToRange(T value, T min, T max) {
 123     return std::min(std::max(value, min), max);
 124   }
 125
 126   // Background: Existing transform code does not do the right thing in
 127   // MapRect / MapQuad / ProjectQuad when there is a perspective projection that
 128   // causes one of the transformed vertices to go to w < 0. In those cases, it
 129   // is necessary to perform clipping in homogeneous coordinates, after applying
 130   // the transform, before dividing-by-w to convert to cartesian coordinates.
 131   //
 132   // These functions return the axis-aligned rect that encloses the correctly
 133   // clipped, transformed polygon.
 134   static gfx::Rect MapEnclosingClippedRect(const gfx::Transform& transform,
 135                                            const gfx::Rect& rect);
 136   static gfx::RectF MapClippedRect(const gfx::Transform& transform,
 137                                    const gfx::RectF& rect);
 138   static gfx::Rect ProjectEnclosingClippedRect(const gfx::Transform& transform,
 139                                                const gfx::Rect& rect);
 140   static gfx::RectF ProjectClippedRect(const gfx::Transform& transform,
 141                                        const gfx::RectF& rect);
 142
 143   // This function is only valid when the transform preserves 2d axis
 144   // alignment and the resulting rect will not be clipped.
 145   static gfx::Rect MapEnclosedRectWith2dAxisAlignedTransform(
 146       const gfx::Transform& transform,
 147       const gfx::Rect& rect);
 148
 149   // Returns an array of vertices that represent the clipped polygon. After
 150   // returning, indexes from 0 to num_vertices_in_clipped_quad are valid in the
 151   // clipped_quad array. Note that num_vertices_in_clipped_quad may be zero,
 152   // which means the entire quad was clipped, and none of the vertices in the
 153   // array are valid.
 154   static void MapClippedQuad(const gfx::Transform& transform,
 155                              const gfx::QuadF& src_quad,
 156                              gfx::PointF clipped_quad[8],
 157                              int* num_vertices_in_clipped_quad);
 158   static bool MapClippedQuad3d(const gfx::Transform& transform,
 159                                const gfx::QuadF& src_quad,
 160                                gfx::Point3F clipped_quad[8],
 161                                int* num_vertices_in_clipped_quad);
 162
 163   static gfx::RectF ComputeEnclosingRectOfVertices(const gfx::PointF vertices[],
 164                                                    int num_vertices);
 165   static gfx::RectF ComputeEnclosingClippedRect(
 166       const HomogeneousCoordinate& h1,
 167       const HomogeneousCoordinate& h2,
 168       const HomogeneousCoordinate& h3,
 169       const HomogeneousCoordinate& h4);
 170
 171   // NOTE: These functions do not do correct clipping against w = 0 plane, but
 172   // they correctly detect the clipped condition via the boolean clipped.
 173   static gfx::QuadF MapQuad(const gfx::Transform& transform,
 174                             const gfx::QuadF& quad,
 175                             bool* clipped);
 176   static gfx::QuadF MapQuad3d(const gfx::Transform& transform,
 177                               const gfx::QuadF& q,
 178                               gfx::Point3F* p,
 179                               bool* clipped);
 180   static gfx::PointF MapPoint(const gfx::Transform& transform,
 181                               const gfx::PointF& point,
 182                               bool* clipped);
 183   static gfx::Point3F MapPoint(const gfx::Transform&,
 184                                const gfx::Point3F&,
 185                                bool* clipped);
 186   static gfx::QuadF ProjectQuad(const gfx::Transform& transform,
 187                                 const gfx::QuadF& quad,
 188                                 bool* clipped);
 189   static gfx::PointF ProjectPoint(const gfx::Transform& transform,
 190                                   const gfx::PointF& point,
 191                                   bool* clipped);
 192   // Identical to the above function, but coerces the homogeneous coordinate to
 193   // a 3d rather than a 2d point.
 194   static gfx::Point3F ProjectPoint3D(const gfx::Transform& transform,
 195                                      const gfx::PointF& point,
 196                                      bool* clipped);
 197
 198   static gfx::Vector2dF ComputeTransform2dScaleComponents(const gfx::Transform&,
 199                                                           float fallbackValue);
 200
 201   // Makes a rect that has the same relationship to input_outer_rect as
 202   // scale_inner_rect has to scale_outer_rect. scale_inner_rect should be
 203   // contained within scale_outer_rect, and likewise the rectangle that is
 204   // returned will be within input_outer_rect at a similar relative, scaled
 205   // position.
 206   static gfx::RectF ScaleRectProportional(const gfx::RectF& input_outer_rect,
 207                                           const gfx::RectF& scale_outer_rect,
 208                                           const gfx::RectF& scale_inner_rect);
 209
 210   // Returns the smallest angle between the given two vectors in degrees.
 211   // Neither vector is assumed to be normalized.
 212   static float SmallestAngleBetweenVectors(const gfx::Vector2dF& v1,
 213                                            const gfx::Vector2dF& v2);
 214
 215   // Projects the |source| vector onto |destination|. Neither vector is assumed
 216   // to be normalized.
 217   static gfx::Vector2dF ProjectVector(const gfx::Vector2dF& source,
 218                                       const gfx::Vector2dF& destination);
 219
 220   // Conversion to value.
 221   static scoped_ptr<base::Value> AsValue(const gfx::Size& s);
 222   static scoped_ptr<base::Value> AsValue(const gfx::Rect& r);
 223   static bool FromValue(const base::Value*, gfx::Rect* out_rect);
 224   static scoped_ptr<base::Value> AsValue(const gfx::PointF& q);
 225
 226   static void AddToTracedValue(const char* name,
 227                                const gfx::Size& s,
 228                                base::trace_event::TracedValue* res);
 229   static void AddToTracedValue(const char* name,
 230                                const gfx::SizeF& s,
 231                                base::trace_event::TracedValue* res);
 232   static void AddToTracedValue(const char* name,
 233                                const gfx::Rect& r,
 234                                base::trace_event::TracedValue* res);
 235   static void AddToTracedValue(const char* name,
 236                                const gfx::PointF& q,
 237                                base::trace_event::TracedValue* res);
 238   static void AddToTracedValue(const char* name,
 239                                const gfx::Point3F&,
 240                                base::trace_event::TracedValue* res);
 241   static void AddToTracedValue(const char* name,
 242                                const gfx::Vector2d& v,
 243                                base::trace_event::TracedValue* res);
 244   static void AddToTracedValue(const char* name,
 245                                const gfx::Vector2dF& v,
 246                                base::trace_event::TracedValue* res);
 247   static void AddToTracedValue(const char* name,
 248                                const gfx::ScrollOffset& v,
 249                                base::trace_event::TracedValue* res);
 250   static void AddToTracedValue(const char* name,
 251                                const gfx::QuadF& q,
 252                                base::trace_event::TracedValue* res);
 253   static void AddToTracedValue(const char* name,
 254                                const gfx::RectF& rect,
 255                                base::trace_event::TracedValue* res);
 256   static void AddToTracedValue(const char* name,
 257                                const gfx::Transform& transform,
 258                                base::trace_event::TracedValue* res);
 259   static void AddToTracedValue(const char* name,
 260                                const gfx::BoxF& box,
 261                                base::trace_event::TracedValue* res);
 262
 263   // Returns a base::Value representation of the floating point value.
 264   // If the value is inf, returns max double/float representation.
 265   static double AsDoubleSafely(double value);
 266   static float AsFloatSafely(float value);
 267
 268   // Returns vector that x axis (1,0,0) transforms to under given transform.
 269   static gfx::Vector3dF GetXAxis(const gfx::Transform& transform);
 270
 271   // Returns vector that y axis (0,1,0) transforms to under given transform.
 272   static gfx::Vector3dF GetYAxis(const gfx::Transform& transform);
 273 };
 274
 275 }  // namespace cc
 276
 277 #endif  // CC_BASE_MATH_UTIL_H_