0
我試圖理解這個函數的功能。它是由我的老師給出的，我無法理解，發現x和y座標的公式背後的邏輯是什麼。從我的數學課我知道我的公式發現攔截，但它的混亂翻譯成代碼。所以我有一些問題，他們如何定義a，b，c的公式以及查找座標x和y。查找線和圓的交點
void Intersection::getIntersectionPoints(const Arc& arc, const Line& line) {
double a, b, c, mu, det;
std::pair<double, double> xPoints;
std::pair<double, double> yPoints;
std::pair<double, double> zPoints;
//(m2+1)x2+2(mc−mq−p)x+(q2−r2+p2−2cq+c2)=0.
//a= m2;
//b= 2 * (mc - mq - p);
//c= q2−r2+p2−2cq+c2
a = pow((line.end().x - line.start().x), 2) + pow((line.end().y - line.start().y), 2) + pow((line.end().z - line.start().z), 2);
b = 2 * ((line.end().x - line.start().x)*(line.start().x - arc.center().x)
+ (line.end().y - line.start().y)*(line.start().y - arc.center().y)
+ (line.end().z - line.start().z)*(line.start().z - arc.center().z));
c = pow((arc.center().x), 2) + pow((arc.center().y), 2) +
pow((arc.center().z), 2) + pow((line.start().x), 2) +
pow((line.start().y), 2) + pow((line.start().z), 2) -
2 * (arc.center().x * line.start().x + arc.center().y * line.start().y +
arc.center().z * line.start().z) - pow((arc.radius()), 2);
det = pow(b, 2) - 4 * a * c;
/* Tangenta na kružnicu */
if (Math<double>::isEqual(det, 0.0, 0.00001)) {
if (!Math<double>::isEqual(a, 0.0, 0.00001))
mu = -b/(2 * a);
else
mu = 0.0;
// x = h + t * (p − h)
xPoints.second = xPoints.first = line.start().x + mu * (line.end().x - line.start().x);
yPoints.second = yPoints.first = line.start().y + mu * (line.end().y - line.start().y);
zPoints.second = zPoints.first = line.start().z + mu * (line.end().z - line.start().z);
}
if (Math<double>::isGreater(det, 0.0, 0.00001)) {
// first intersection
mu = (-b - sqrt(pow(b, 2) - 4 * a * c))/(2 * a);
xPoints.first = line.start().x + mu * (line.end().x - line.start().x);
yPoints.first = line.start().y + mu * (line.end().y - line.start().y);
zPoints.first = line.start().z + mu * (line.end().z - line.start().z);
// second intersection
mu = (-b + sqrt(pow(b, 2) - 4 * a * c))/(2 * a);
xPoints.second = line.start().x + mu * (line.end().x - line.start().x);
yPoints.second = line.start().y + mu * (line.end().y - line.start().y);
zPoints.second = line.start().z + mu * (line.end().z - line.start().z);
}