/*
* Copyright 2008 The Android Open Source Project
*
* Use of this source code is governed by a BSD-style license that can be
* found in the LICENSE file.
*/
#include "SkMathPriv.h"
#include "SkPointPriv.h"
#if 0
void SkIPoint::rotateCW(SkIPoint* dst) const {
SkASSERT(dst);
// use a tmp in case this == dst
int32_t tmp = fX;
dst->fX = -fY;
dst->fY = tmp;
}
void SkIPoint::rotateCCW(SkIPoint* dst) const {
SkASSERT(dst);
// use a tmp in case this == dst
int32_t tmp = fX;
dst->fX = fY;
dst->fY = -tmp;
}
#endif
///////////////////////////////////////////////////////////////////////////////
void SkPoint::scale(SkScalar scale, SkPoint* dst) const {
SkASSERT(dst);
dst->set(fX * scale, fY * scale);
}
bool SkPoint::normalize() {
return this->setLength(fX, fY, SK_Scalar1);
}
bool SkPoint::setNormalize(SkScalar x, SkScalar y) {
return this->setLength(x, y, SK_Scalar1);
}
bool SkPoint::setLength(SkScalar length) {
return this->setLength(fX, fY, length);
}
// Returns the square of the Euclidian distance to (dx,dy).
static inline float getLengthSquared(float dx, float dy) {
return dx * dx + dy * dy;
}
// Calculates the square of the Euclidian distance to (dx,dy) and stores it in
// *lengthSquared. Returns true if the distance is judged to be "nearly zero".
//
// This logic is encapsulated in a helper method to make it explicit that we
// always perform this check in the same manner, to avoid inconsistencies
// (see http://code.google.com/p/skia/issues/detail?id=560 ).
static inline bool is_length_nearly_zero(float dx, float dy,
float *lengthSquared) {
*lengthSquared = getLengthSquared(dx, dy);
return *lengthSquared <= (SK_ScalarNearlyZero * SK_ScalarNearlyZero);
}
SkScalar SkPoint::Normalize(SkPoint* pt) {
float x = pt->fX;
float y = pt->fY;
float mag2;
if (is_length_nearly_zero(x, y, &mag2)) {
pt->set(0, 0);
return 0;
}
float mag, scale;
if (SkScalarIsFinite(mag2)) {
mag = sk_float_sqrt(mag2);
scale = 1 / mag;
} else {
// our mag2 step overflowed to infinity, so use doubles instead.
// much slower, but needed when x or y are very large, other wise we
// divide by inf. and return (0,0) vector.
double xx = x;
double yy = y;
double magmag = sqrt(xx * xx + yy * yy);
mag = (float)magmag;
// we perform the divide with the double magmag, to stay exactly the
// same as setLength. It would be faster to perform the divide with
// mag, but it is possible that mag has overflowed to inf. but still
// have a non-zero value for scale (thanks to denormalized numbers).
scale = (float)(1 / magmag);
}
pt->set(x * scale, y * scale);
return mag;
}
SkScalar SkPoint::Length(SkScalar dx, SkScalar dy) {
float mag2 = dx * dx + dy * dy;
if (SkScalarIsFinite(mag2)) {
return sk_float_sqrt(mag2);
} else {
double xx = dx;
double yy = dy;
return sk_double_to_float(sqrt(xx * xx + yy * yy));
}
}
/*
* We have to worry about 2 tricky conditions:
* 1. underflow of mag2 (compared against nearlyzero^2)
* 2. overflow of mag2 (compared w/ isfinite)
*
* If we underflow, we return false. If we overflow, we compute again using
* doubles, which is much slower (3x in a desktop test) but will not overflow.
*/
bool SkPoint::setLength(float x, float y, float length) {
float mag2;
if (is_length_nearly_zero(x, y, &mag2)) {
this->set(0, 0);
return false;
}
float scale;
if (SkScalarIsFinite(mag2)) {
scale = length / sk_float_sqrt(mag2);
} else {
// our mag2 step overflowed to infinity, so use doubles instead.
// much slower, but needed when x or y are very large, other wise we
// divide by inf. and return (0,0) vector.
double xx = x;
double yy = y;
#ifdef SK_CPU_FLUSH_TO_ZERO
// The iOS ARM processor discards small denormalized numbers to go faster.
// Casting this to a float would cause the scale to go to zero. Keeping it
// as a double for the multiply keeps the scale non-zero.
double dscale = length / sqrt(xx * xx + yy * yy);
fX = x * dscale;
fY = y * dscale;
return true;
#else
scale = (float)(length / sqrt(xx * xx + yy * yy));
#endif
}
fX = x * scale;
fY = y * scale;
return true;
}
bool SkPointPriv::SetLengthFast(SkPoint* pt, float length) {
float mag2;
if (is_length_nearly_zero(pt->fX, pt->fY, &mag2)) {
pt->set(0, 0);
return false;
}
float scale;
if (SkScalarIsFinite(mag2)) {
scale = length * sk_float_rsqrt(mag2); // <--- this is the difference
} else {
// our mag2 step overflowed to infinity, so use doubles instead.
// much slower, but needed when x or y are very large, other wise we
// divide by inf. and return (0,0) vector.
double xx = pt->fX;
double yy = pt->fY;
scale = (float)(length / sqrt(xx * xx + yy * yy));
}
pt->fX *= scale;
pt->fY *= scale;
return true;
}
///////////////////////////////////////////////////////////////////////////////
SkScalar SkPointPriv::DistanceToLineBetweenSqd(const SkPoint& pt, const SkPoint& a,
const SkPoint& b,
Side* side) {
SkVector u = b - a;
SkVector v = pt - a;
SkScalar uLengthSqd = LengthSqd(u);
SkScalar det = u.cross(v);
if (side) {
SkASSERT(-1 == kLeft_Side &&
0 == kOn_Side &&
1 == kRight_Side);
*side = (Side) SkScalarSignAsInt(det);
}
SkScalar temp = det / uLengthSqd;
temp *= det;
return temp;
}
SkScalar SkPointPriv::DistanceToLineSegmentBetweenSqd(const SkPoint& pt, const SkPoint& a,
const SkPoint& b) {
// See comments to distanceToLineBetweenSqd. If the projection of c onto
// u is between a and b then this returns the same result as that
// function. Otherwise, it returns the distance to the closer of a and
// b. Let the projection of v onto u be v'. There are three cases:
// 1. v' points opposite to u. c is not between a and b and is closer
// to a than b.
// 2. v' points along u and has magnitude less than y. c is between
// a and b and the distance to the segment is the same as distance
// to the line ab.
// 3. v' points along u and has greater magnitude than u. c is not
// not between a and b and is closer to b than a.
// v' = (u dot v) * u / |u|. So if (u dot v)/|u| is less than zero we're
// in case 1. If (u dot v)/|u| is > |u| we are in case 3. Otherwise
// we're in case 2. We actually compare (u dot v) to 0 and |u|^2 to
// avoid a sqrt to compute |u|.
SkVector u = b - a;
SkVector v = pt - a;
SkScalar uLengthSqd = LengthSqd(u);
SkScalar uDotV = SkPoint::DotProduct(u, v);
if (uDotV <= 0) {
return LengthSqd(v);
} else if (uDotV > uLengthSqd) {
return DistanceToSqd(b, pt);
} else {
SkScalar det = u.cross(v);
SkScalar temp = det / uLengthSqd;
temp *= det;
return temp;
}
}