diff options
Diffstat (limited to 'geom.hpp')
| -rw-r--r-- | geom.hpp | 63 |
1 files changed, 31 insertions, 32 deletions
@@ -2,6 +2,9 @@ #include <math.h> +#define EPSILON 1e-6 +#define abs(x) ((x)<0?-(x):(x)) + struct vec { double x, y; @@ -10,6 +13,9 @@ struct vec { double norm() const { return sqrt(x*x + y*y); } + double sqnorm() const { + return x*x + y*y; + } double sqnorm() const { return x*x + y*y; @@ -27,33 +33,20 @@ struct vec { } bool is_nil() const { - return x == 0 && y == 0; - } - - vec operator+ (const vec& o) const { - return vec(x + o.x, y + o.y); - } - vec operator- (const vec& o) const { - return vec(x - o.x, y - o.y); - } - vec operator* (double m) const { - return vec(m * x, m * y); - } - vec operator/ (double m) const { - return vec(m / x, m / y); + return sqnorm() < EPSILON; } static vec from_polar(double r, double theta) { return vec(r * cos(theta), r * sin(theta)); } - static vec dot(vec a, vec b) { // dot product (produit scalaire) + static double dot(vec a, vec b) { // dot product (produit scalaire) return a.x * b.x + a.y * b.y; } - static vec cross(vec a, vec b) { // cross product (déterminant 2x2) + static double cross(vec a, vec b) { // cross product (déterminant 2x2) return a.x * b.y - a.y * b.x; } - static vec angle(vec a, vec b) { // oriented angle between two vectors + static double angle(vec a, vec b) { // oriented angle between two vectors if (a.is_nil() || b.is_nil()) return 0; float cos = dot(a.normalize(), b.normalize()); if (cos <= -1) return M_PI; @@ -66,6 +59,13 @@ struct vec { } }; +inline vec operator+(const vec& a, const vec& b) { return vec(a.x+b.x, a.y+b.y); } +inline vec operator-(const vec& a, const vec& b) { return vec(a.x-b.x, a.y-b.y); } +inline vec operator-(const vec& a) { return vec(-a.x, -a.y); } +inline vec operator*(double a, const vec& v) { return vec(a*v.x, a*v.y); } +inline vec operator*(const vec& v, double a) { return vec(a*v.x, a*v.y); } +inline vec operator/(const vec& v, double a) { return vec(v.x/a, v.y/a); } + struct line { // Line defined by ax + by + c = 0 double a, b, c; @@ -78,21 +78,21 @@ struct line { } bool on_line(vec p) const { - return a * p.x + b * p.y + c == 0; + return a * p.x + b * p.y + c < EPSILON; } double dist(vec p) const { // calculate distance from p to the line - return abs(a*p.x+b*p.y+c)/sqrt(a*a+b*b); + return abs(a*p.x + b*p.y + c) / sqrt(a*a + b*b); } - vec dir() const { + vec dir() const { // calculate a directional vector oh the line return vec(-b,a); - } + } vec proj(vec p) const { // calculate orthogonal projection of point p on the line - return p-(a*p.x+b*p.y+c)/(a*a+b*b)*vec(a,b); + return p-(a*p.x+b*p.y+c)/(a*a+b*b)*vec(a,b); } double angle() const { @@ -108,18 +108,17 @@ struct segment { bool on_segment(vec p) const { // TODO - + // does point intersect segment? return false; } double dist(vec p) const { - double scal = vec::dot(b-a, p-a); - double sqn = (b-a).sqnorm - if(scal > sqn)return (p-b).norm ; - if(scal < 0) return (p-a).norm ; - return line(a,b).dist(p); - return 1; + double scal = vec::dot(b-a, p-a); + double sqn = (b-a).sqnorm + if(scal > sqn)return (p-b).norm ; + if(scal < 0) return (p-a).norm ; + return line(a,b).dist(p); } }; @@ -130,8 +129,8 @@ struct circle { circle(double x, double y, double rr) : c(x, y), r(rr) {} circle(vec cc, double rr) : c(cc), r(rr) {} - bool on_circle(vec.p) const { - return ((p - c).norm() == r); + bool on_circle(vec p) const { + return ((p - c).norm() - r < EPSILON); } double dist(vec p) const { @@ -145,7 +144,7 @@ struct circpoint { double theta; circpoint(circle cc, double th) : c(cc), theta(th) {} - circpoint(vec cc, double rr, double th : c(cc, rr), theta(th) {} + circpoint(vec cc, double rr, double th) : c(cc, rr), theta(th) {} vec pos() const { return c.c + vec(c.r * cos(theta), c.r * sin(theta)); |