| /* |
| * 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 "SkPoint.h" |
| |
| 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; |
| } |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| void SkPoint::rotateCW(SkPoint* dst) const { |
| SkASSERT(dst); |
| |
| // use a tmp in case this == dst |
| SkScalar tmp = fX; |
| dst->fX = -fY; |
| dst->fY = tmp; |
| } |
| |
| void SkPoint::rotateCCW(SkPoint* dst) const { |
| SkASSERT(dst); |
| |
| // use a tmp in case this == dst |
| SkScalar tmp = fX; |
| dst->fX = fY; |
| dst->fY = -tmp; |
| } |
| |
| 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 SkPoint::setLengthFast(float length) { |
| return this->setLengthFast(fX, fY, length); |
| } |
| |
| bool SkPoint::setLengthFast(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_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 = x; |
| double yy = y; |
| scale = (float)(length / sqrt(xx * xx + yy * yy)); |
| } |
| fX = x * scale; |
| fY = y * scale; |
| return true; |
| } |
| |
| |
| /////////////////////////////////////////////////////////////////////////////// |
| |
| SkScalar SkPoint::distanceToLineBetweenSqd(const SkPoint& a, |
| const SkPoint& b, |
| Side* side) const { |
| |
| SkVector u = b - a; |
| SkVector v = *this - a; |
| |
| SkScalar uLengthSqd = u.lengthSqd(); |
| SkScalar det = u.cross(v); |
| if (side) { |
| SkASSERT(-1 == SkPoint::kLeft_Side && |
| 0 == SkPoint::kOn_Side && |
| 1 == kRight_Side); |
| *side = (Side) SkScalarSignAsInt(det); |
| } |
| SkScalar temp = det / uLengthSqd; |
| temp *= det; |
| return temp; |
| } |
| |
| SkScalar SkPoint::distanceToLineSegmentBetweenSqd(const SkPoint& a, |
| const SkPoint& b) const { |
| // 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 = *this - a; |
| |
| SkScalar uLengthSqd = u.lengthSqd(); |
| SkScalar uDotV = SkPoint::DotProduct(u, v); |
| |
| if (uDotV <= 0) { |
| return v.lengthSqd(); |
| } else if (uDotV > uLengthSqd) { |
| return b.distanceToSqd(*this); |
| } else { |
| SkScalar det = u.cross(v); |
| SkScalar temp = det / uLengthSqd; |
| temp *= det; |
| return temp; |
| } |
| } |