B-spline Curve in c++ - c++

Question

Could anyone help me about B-spline Curve error?
I want to draw B-spline Curve in c++, but even though all coordinates are positive, the segment's coordinate is negative.
This is B-spline Curve code.
void BSplineCurve(Dot &ControlPoint1, Dot &ControlPoint2,
Dot &ControlPoint3,Dot &ControlPoint4,
Dot &DrawCurve, double &t){
double t2 = t * t;
double t3 = t2 * t;
double mt3 = (1 - t) * (1 - t) * (1 - t);
double bi3 = mt3 / 6;
double bi2 = ((3 * t3) - (6 * t2) + 4) / 6;
double bi1 = ((-3 * t3) + (3 * t2) + (3 * t) + 1) / 6;
double bi = mt3 / 6;
DrawCurve.x = ControlPoint1.x * bi3;
DrawCurve.x += ControlPoint2.x * bi2;
DrawCurve.x += ControlPoint3.x * bi1;
DrawCurve.x += ControlPoint4.x * bi;
DrawCurve.y = ControlPoint1.y * bi3;
DrawCurve.y += ControlPoint2.y * bi2;
DrawCurve.y += ControlPoint3.y * bi1;
DrawCurve.y += ControlPoint4.y * bi;
}
This is Drawing Code.
double t = 3.f;
do{
if ((3 < t) && (t <= 4)) {
BSplineCurve(ControlPoint1, ControlPoint2, ControlPoint3, ControlPoint4, DrawCurve, t);
Draw1Dot(DrawCurve.x, DrawCurve.y, DrawCurve.R, DrawCurve.G, DrawCurve.B);
}
else if ((4 < t) && (t <= 5)) {
BSplineCurve(ControlPoint2, ControlPoint3, ControlPoint4, ControlPoint5, DrawCurve, t);
Draw1Dot(DrawCurve.x, DrawCurve.y, DrawCurve.R, DrawCurve.G, DrawCurve.B);
}
else if ((5 < t) && (t <= 6)) {
BSplineCurve(ControlPoint3, ControlPoint4, ControlPoint5, ControlPoint6, DrawCurve, t);
Draw1Dot(DrawCurve.x, DrawCurve.y, DrawCurve.R, DrawCurve.G, DrawCurve.B);
}
t += 0.001;
} while(t < 6.001);
This is Control Point's coordinate.
Poiont1 : 50, 50
Poiont2 : 50, 100
Poiont3 : 200, 100
Poiont4 : 200, 50
Poiont5 : 350, 50
Poiont6 : 350, 100
But this is 1st segment's coordinate.
Q3 : -1543, -349

Answer 1

Your drawing code looks wrong.
In function BSplineCurve the t parameter should take values in [0, 1] range. By changing t from 0 to 1 one will build a cubic B-spline between points ControlPoint2 and ControlPoint3.
You could try something like:
Dot points[6] = {ControlPoint1, ControlPoint2, ControlPoint3, ControlPoint4, ControlPoint5, ControlPoint6};
for(double t = 3.0; t < 6.0; t += 0.001)
{
const int start = static_cast<int>(t);
BSplineCurve(points[start - 3],
points[start - 2],
points[start - 1],
points[start],
DrawCurve,
t - start);
Draw1Dot(DrawCurve.x, DrawCurve.y, DrawCurve.R, DrawCurve.G, DrawCurve.B);
}
Update
Your B-spline calculation code looks wrong too :-)
bi should be t3/6.0 and not mt3/6.0. See here (slide 25).
The fixed function can look something like this (I did not test it):
void BSplineCurve(const Dot &point1,
const Dot &point2,
const Dot &point3,
const Dot &point4,
const double t,
Dot &result)
{
const double t2 = t * t;
const double t3 = t2 * t;
const double mt = 1.0 - t;
const double mt3 = mt * mt * mt;
const double bi3 = mt3;
const double bi2 = 3 * t3 - 6 * t2 + 4;
const double bi1 =-3 * t3 + 3 * t2 + 3 * t + 1;
const double bi = t3;
result.x = point1.x * bi3 +
point2.x * bi2 +
point3.x * bi1 +
point4.x * bi;
result.x /= 6.0;
result.y = point1.y * bi3 +
point2.y * bi2 +
point3.y * bi1 +
point4.y * bi;
result.y /= 6.0;
}

Answer 2

Maybe the point you use is too very close. In spline it is not good iidea to use very close point. becaue so we have very "galloping" curve. Like this:
red is original