/* * vector3.cpp * Copyright (C) Andrew Tridgell 2012 * * This file is free software: you can redistribute it and/or modify it * under the terms of the GNU General Public License as published by the * Free Software Foundation, either version 3 of the License, or * (at your option) any later version. * * This file is distributed in the hope that it will be useful, but * WITHOUT ANY WARRANTY; without even the implied warranty of * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. * See the GNU General Public License for more details. * * You should have received a copy of the GNU General Public License along * with this program. If not, see <http://www.gnu.org/licenses/>. */ #pragma GCC optimize("O3") #include "AP_Math.h" template <typename T> float Vector2<T>::length(void) const { return norm(x, y); } // dot product template <typename T> T Vector2<T>::operator *(const Vector2<T> &v) const { return x*v.x + y*v.y; } // cross product template <typename T> T Vector2<T>::operator %(const Vector2<T> &v) const { return x*v.y - y*v.x; } template <typename T> Vector2<T> &Vector2<T>::operator *=(const T num) { x*=num; y*=num; return *this; } template <typename T> Vector2<T> &Vector2<T>::operator /=(const T num) { x /= num; y /= num; return *this; } template <typename T> Vector2<T> &Vector2<T>::operator -=(const Vector2<T> &v) { x -= v.x; y -= v.y; return *this; } template <typename T> bool Vector2<T>::is_nan(void) const { return isnan(x) || isnan(y); } template <typename T> bool Vector2<T>::is_inf(void) const { return isinf(x) || isinf(y); } template <typename T> Vector2<T> &Vector2<T>::operator +=(const Vector2<T> &v) { x+=v.x; y+=v.y; return *this; } template <typename T> Vector2<T> Vector2<T>::operator /(const T num) const { return Vector2<T>(x/num, y/num); } template <typename T> Vector2<T> Vector2<T>::operator *(const T num) const { return Vector2<T>(x*num, y*num); } template <typename T> Vector2<T> Vector2<T>::operator -(const Vector2<T> &v) const { return Vector2<T>(x-v.x, y-v.y); } template <typename T> Vector2<T> Vector2<T>::operator +(const Vector2<T> &v) const { return Vector2<T>(x+v.x, y+v.y); } template <typename T> Vector2<T> Vector2<T>::operator -(void) const { return Vector2<T>(-x,-y); } template <typename T> bool Vector2<T>::operator ==(const Vector2<T> &v) const { return (is_equal(x,v.x) && is_equal(y,v.y)); } template <typename T> bool Vector2<T>::operator !=(const Vector2<T> &v) const { return (!is_equal(x,v.x) || !is_equal(y,v.y)); } template <typename T> float Vector2<T>::angle(const Vector2<T> &v2) const { float len = this->length() * v2.length(); if (len <= 0) { return 0.0f; } float cosv = ((*this)*v2) / len; if (cosv >= 1) { return 0.0f; } if (cosv <= -1) { return M_PI; } return acosf(cosv); } // find the intersection between two line segments // returns true if they intersect, false if they do not // the point of intersection is returned in the intersection argument template <typename T> bool Vector2<T>::segment_intersection(const Vector2<T>& seg1_start, const Vector2<T>& seg1_end, const Vector2<T>& seg2_start, const Vector2<T>& seg2_end, Vector2<T>& intersection) { // implementation borrowed from http://stackoverflow.com/questions/563198/how-do-you-detect-where-two-line-segments-intersect const Vector2<T> r1 = seg1_end - seg1_start; const Vector2<T> r2 = seg2_end - seg2_start; const Vector2<T> ss2_ss1 = seg2_start - seg1_start; const float r1xr2 = r1 % r2; const float q_pxr = ss2_ss1 % r1; if (fabsf(r1xr2) < FLT_EPSILON) { // either collinear or parallel and non-intersecting return false; } else { // t = (q - p) * s / (r * s) // u = (q - p) * r / (r * s) float t = (ss2_ss1 % r2) / r1xr2; float u = q_pxr / r1xr2; if ((u >= 0) && (u <= 1) && (t >= 0) && (t <= 1)) { // lines intersect // t can be any non-negative value because (p, p + r) is a ray // u must be between 0 and 1 because (q, q + s) is a line segment intersection = seg1_start + (r1*t); return true; } else { // non-parallel and non-intersecting return false; } } } // find the intersection between a line segment and a circle // returns true if they intersect and intersection argument is updated with intersection closest to seg_start // solution adapted from http://stackoverflow.com/questions/1073336/circle-line-segment-collision-detection-algorithm template <typename T> bool Vector2<T>::circle_segment_intersection(const Vector2<T>& seg_start, const Vector2<T>& seg_end, const Vector2<T>& circle_center, float radius, Vector2<T>& intersection) { // calculate segment start and end as offsets from circle's center const Vector2f seg_start_local = seg_start - circle_center; // calculate vector from start to end const Vector2f seg_end_minus_start = seg_end - seg_start; const float a = sq(seg_end_minus_start.x) + sq(seg_end_minus_start.y); const float b = 2 * ((seg_end_minus_start.x * seg_start_local.x) + (seg_end_minus_start.y * seg_start_local.y)); const float c = sq(seg_start_local.x) + sq(seg_start_local.y) - sq(radius); const float delta = sq(b) - (4.0f * a * c); // check for invalid data if (::is_zero(a)) { return false; } if (isnan(a) || isnan(b) || isnan(c) || isnan(delta)) { return false; } // check for invalid delta (i.e. discriminant) if (delta < 0.0f) { return false; } const float delta_sqrt = sqrtf(delta); const float t1 = (-b + delta_sqrt) / (2.0f * a); const float t2 = (-b - delta_sqrt) / (2.0f * a); // Three hit cases: // -o-> --|--> | | --|-> // Impale(t1 hit,t2 hit), Poke(t1 hit,t2>1), ExitWound(t1<0, t2 hit), // Three miss cases: // -> o o -> | -> | // FallShort (t1>1,t2>1), Past (t1<0,t2<0), CompletelyInside(t1<0, t2>1) // intersection = new Vector3(E.x + t1 * d.x, secondPoint.y, E.y + t1 * d.y); // intersection.x = seg_start.x + t1 * seg_end_minus_start.x; // intersection.y = seg_start.y + t1 * seg_end_minus_start.y; if ((t1 >= 0.0f) && (t1 <= 1.0f)) { // t1 is the intersection, and it is closer than t2 (since t1 uses -b - discriminant) // Impale, Poke intersection = seg_start + (seg_end_minus_start * t1); return true; } // here t1 did not intersect so we are either started inside the sphere or completely past it if ((t2 >= 0.0f) && (t2 <= 1.0f)) { // ExitWound intersection = seg_start + (seg_end_minus_start * t2); return true; } // no intersection: FallShort, Past or CompletelyInside return false; } // only define for float template float Vector2<float>::length(void) const; template float Vector2<float>::operator *(const Vector2<float> &v) const; template float Vector2<float>::operator %(const Vector2<float> &v) const; template Vector2<float> &Vector2<float>::operator *=(const float num); template Vector2<float> &Vector2<float>::operator /=(const float num); template Vector2<float> &Vector2<float>::operator -=(const Vector2<float> &v); template Vector2<float> &Vector2<float>::operator +=(const Vector2<float> &v); template Vector2<float> Vector2<float>::operator /(const float num) const; template Vector2<float> Vector2<float>::operator *(const float num) const; template Vector2<float> Vector2<float>::operator +(const Vector2<float> &v) const; template Vector2<float> Vector2<float>::operator -(const Vector2<float> &v) const; template Vector2<float> Vector2<float>::operator -(void) const; template bool Vector2<float>::operator ==(const Vector2<float> &v) const; template bool Vector2<float>::operator !=(const Vector2<float> &v) const; template bool Vector2<float>::is_nan(void) const; template bool Vector2<float>::is_inf(void) const; template float Vector2<float>::angle(const Vector2<float> &v) const; template bool Vector2<float>::segment_intersection(const Vector2<float>& seg1_start, const Vector2<float>& seg1_end, const Vector2<float>& seg2_start, const Vector2<float>& seg2_end, Vector2<float>& intersection); template bool Vector2<float>::circle_segment_intersection(const Vector2<float>& seg_start, const Vector2<float>& seg_end, const Vector2<float>& circle_center, float radius, Vector2<float>& intersection); template bool Vector2<long>::operator ==(const Vector2<long> &v) const; // define for int template bool Vector2<int>::operator ==(const Vector2<int> &v) const;