Who can explain in detail some of the functions AIRealBezierSuite

Question

AIAPI void(*  Tangent )(AIRealBezier *b, AIReal t, AIRealPoint *v)    Finds a tangent for a given input to a cubic Bezier.
AIAPI void(*  Normal )(AIRealBezier *b, AIReal t, AIRealPoint *v)    Finds the normal for a given input to a cubic Bezier.
AIAPI AIBoolean(*  IntersectsRect )(AIRealBezier *b, AIRealRect *r, AIReal scale)    Reports whether a cubic Bezier intersects a rectangle.
////////////////   this is  my code:
AIRealPoint p0,p1,p2,p3;
p0.h = 50.0;
p0.v = 0;
p1.h = 50.0;
p1.v = -27.614258;
p2.h = 27.614258;
p2.v = -50.0;
p3.h = 0;
p3.v = -50.0;
AIRealBezier bz;
bz.p0 = p0;
bz.p1 = p1;
bz.p2 = p2;
bz.p3 = p3;
//    This bezier curve represents a quarter of the arc
AIRealPoint pt,pn;
sAIRealBezier->Tangent(&bz,0.5,&pt);      // debug output :     pt.h = -18.096436   pt.v = -18.096436
sAIRealBezier->Normal(&bz,0.5,&pn);       // debug output:      pn.h = 18.096436   pn.v = -18.096436
//   I do not understand why the value of  pt.h is -18.096436  , pt.v is -18.096436 ,pn.h is 18.096436  , pn.v is -18.096436
//  AI is how to use a AIRealPoint to represent a tangent？
//  What is Normal?
AIAPI AIBoolean(*  IntersectsRect )(AIRealBezier *b, AIRealRect *r, AIReal scale)    Reports whether a cubic Bezier intersects a rectangle.
I found this function always returns false，who used it yet?

Answer 1

I'm not sure what you find confusing. The AIRealBezier is the four points representing a curve. t is the point along that curve. In both cases, v is the vector springing from the point at t on the curve. Granted, you should probably be using Evaluate() as well to find the point along the curve (unless you're using t=0 or t=1, in which case you don't need to) or PointAndTangent() to get both at the same time.
As for IntersectsRect(), I'm not sure how much I'd trust it anyways. The documentation basically says it draws the curve & the rect and then sees if the pixels intersect. That seems kind of dicey to me (it's probably fine for where its used internally of course). There are ways to calculate the intersection of a bezier with a line; personally, I'd trust those methods more (and we wrote our own code to do just that).