CubicSpline::CubicSpline(vector<Vector3> controlPoints, float tightness, int subDivisions) : m_length(0.f)
{
Vector3 endTangent;
for (int i = 0; i < controlPoints.size()-1; i++) {
vector<Vector3> path;
Vector3 start = controlPoints[i];
Vector3 end = controlPoints[i+1];
path.push_back(start);
if (endTangent != Vector3::Zero) {
// start tangent becomes the negative of the previous end tangent
path.push_back(-endTangent + start);
}
if (i < controlPoints.size() - 2) {
Vector3 next = controlPoints[i + 2];
Vector3 line1 = start - end;
Vector3 line2 = end - next;
line1.Normalize();
line2.Normalize();
// average the two vectors to get the normal of reflection
endTangent = Vector3((line1.x + line2.x) / 2.f, (line1.y + line2.y) / 2.f, (line1.z + line2.z) / 2.f);
//endTangent.Normalize();
endTangent *= tightness;
path.push_back(endTangent + end);
}
path.push_back(end);
Bezier bezier = Bezier(path);
float length = bezier.Length(subDivisions);
m_length += length;
m_bezierSections.push_back(std::make_pair(Bezier(bezier), length));
}
}
void draw_surface(float width, float height)
{
/* pseudo
1. calculate p3-p2
2. set new bezier p0 = old bezier p3
3. new beier p1 = p0 + old(p3-p2)*/
Bezier tl = Bezier(width, height, angle);
Vector4 d1 = tl.p3 - tl.p2;
Vector4 d2 = tl.p7 - tl.p6;
Vector4 d3 = tl.p11 - tl.p10;
Vector4 d4 = tl.p15 - tl.p14;
Vector4 g1 = tl.p3 + d1;
Vector4 g2 = tl.p7 + d2;
Vector4 g3 = tl.p11 + d3;
Vector4 g4 = tl.p15 + d4;
cout << "tlp7: " << tl.p7.y << endl;
Bezier tr = Bezier(tl.p3, g1, tl.p7, g2,
tl.p11, g3, tl.p15, g4, angle);
//cout << "p0: " << tr.p0.y << " p3: " << tr.p3.y << " p12: " << tr.p12.y << " p15: " << tr.p15.y << endl;
cout << "p4: " << tr.p4.y << " p8: " << tr.p8.y << " p7: " << tr.p7.y << " p11: " << tr.p11.y << endl;
cout << "p5: " << tr.p5.y << endl;
for (float t1 = -0.5; t1 < 0.49; t1 += 0.01)
{
for (float t2 = -0.5; t2 < 0.49; t2 += 0.01)
{
glColor3f(1, 0, 0);
tl.tessellate(t1, t2, .1);
glColor3f(0, 0, 1);
tr.tessellate(t1, t2, .1);
}
}
}
void Polygon::Bezier(QImage *backBuffer, double x1, double y1, double x2, double y2, double x3, double y3, double x4, double y4, QColor color){
double m_distance_tolerance = 0.25;
double x12 = (x1 + x2) / 2;
double y12 = (y1 + y2) / 2;
double x23 = (x2 + x3) / 2;
double y23 = (y2 + y3) / 2;
double x34 = (x3 + x4) / 2;
double y34 = (y3 + y4) / 2;
double x123 = (x12 + x23) / 2;
double y123 = (y12 + y23) / 2;
double x234 = (x23 + x34) / 2;
double y234 = (y23 + y34) / 2;
double x1234 = (x123 + x234) / 2;
double y1234 = (y123 + y234) / 2;
double dx = x4 - x1;
double dy = y4-y1;
double d2 = fabs(((x2 - x4) * dy - (y2 - y4) * dx));
double d3 = fabs(((x3 - x4) * dy - (y3 - y4) * dx));
if( (d2 + d3)*(d2 + d3) < m_distance_tolerance * (dx*dx + dy*dy) ){
drawLine(backBuffer, x1, y1, x4, y4, color);
}
else{
Bezier(backBuffer, x1, y1, x12, y12, x123, y123, x1234, y1234, color);
Bezier(backBuffer, x1234, y1234, x234, y234, x34, y34, x4, y4, color);
}
}
double Measurement::NearestPointOnCurve(QPointF P, vector<QPointF> V)
{
QPointF *w; /* Ctl pts for 5th-degree eqn */
double t_candidate[W_DEGREE]; /* Possible roots */
int n_solutions; /* Number of roots found */
double t; /* Parameter value of closest pt*/
QPointF v_arr[4];
for(int i=0; i<4; i++)
v_arr[i]=V[i];
/* Convert problem to 5th-degree Bezier form */
w = ConvertToBezierForm(P, v_arr);
/* Find all possible roots of 5th-degree equation */
n_solutions = FindRoots(w, W_DEGREE, t_candidate, 0);
free((char *)w);
/* Compare distances of P to all candidates, and to t=0, and t=1 */
{
double dist, new_dist;
QPointF p;
QPointF v;
int i;
/* Check distance to beginning of curve, where t = 0 */
dist = V2SquaredLength(V2Sub(&P, &v_arr[0], &v));
t = 0.0;
/* Find distances for candidate points */
for (i = 0; i < n_solutions; i++) {
p = Bezier(v_arr, DEGREE, t_candidate[i],
(QPointF *)NULL, (QPointF *)NULL);
new_dist = V2SquaredLength(V2Sub(&P, &p, &v));
if (new_dist < dist) {
dist = new_dist;
t = t_candidate[i];
}
}
/* Finally, look at distance to end point, where t = 1.0 */
new_dist = V2SquaredLength(V2Sub(&P, &V[DEGREE], &v));
if (new_dist < dist) {
dist = new_dist;
t = 1.0;
}
}
/* Return the point on the curve at parameter value t */
// printf("t : %4.12f\n", t);
QPointF b=Bezier(v_arr, DEGREE, t, (QPointF *)NULL, (QPointF *)NULL);
return V2DistanceBetween2Points(&P,&b);
}
Point Bezier2D(Point p[4][4],float u,float v)
{
float U = 1-u;
float V = 1-v;
Point P;
P.x = Bezier(x);
P.y = Bezier(y);
P.z = Bezier(z);
return P;
}
void setUpCurve(float d)
{
blc = Vector3(-d, 0, -d);
brc = Vector3(d, 0, -d);
trc = Vector3(d, 0, d);
tlc = Vector3(-d, 0, d);
float dist = d / 3;
if (cp == 1)
{
glColor3f(1, 0, 1);
Matrix4 tc;
Matrix4 t;
t.makeTranslate(blc.x, blc.y, blc.z);
tc = objCamera.c;
tc = tc*t;
tc.transpose();
glLoadMatrixd(tc.getPointer());
glutWireSphere(.5, 20, 20);
t.makeTranslate(brc.x, brc.y, brc.z);
tc = objCamera.c;
tc = tc*t;
tc.transpose();
glLoadMatrixd(tc.getPointer());
glutWireSphere(.5, 20, 20);
t.makeTranslate(trc.x, trc.y, trc.z);
tc = objCamera.c;
tc = tc*t;
tc.transpose();
glLoadMatrixd(tc.getPointer());
glutWireSphere(.5, 20, 20);
t.makeTranslate(tlc.x, tlc.y, tlc.z);
tc = objCamera.c;
tc = tc*t;
tc.transpose();
glLoadMatrixd(tc.getPointer());
glutWireSphere(.5, 20, 20);
}
glColor3f(0, 0, 1);
x1 = Bezier(blc, Vector3(-dist, 0, -1.5*d), Vector3(dist, 0, -1.5*d), brc);
glColor3f(1, 1, 0);
x2 = Bezier(brc, Vector3(d*1.5, 0, -dist), Vector3(d*1.5, 0, dist), trc);
glColor3f(1, 0, 0);
x3 = Bezier(trc, Vector3(dist, 0, 1.5*d), Vector3(-dist, 0, 1.5*d), tlc);
glColor3f(1, 1, 1);
x4 = Bezier(tlc, Vector3(-1.5*d, 0, dist), Vector3(-1.5*d, 0, -dist), blc);
}
/* findHorizontal:
* Given 4 Bezier control points pts, corresponding to the portion
* of an initial spline with path parameter in the range
* 0.0 <= tmin <= t <= tmax <= 1.0, return t where the spline
* first crosses a horizontal line segment
* [(xmin,ycoord),(xmax,ycoord)]. Return -1 if not found.
* This is done by binary subdivision.
*/
static double
findHorizontal(pointf * pts, double tmin, double tmax,
double ycoord, double xmin, double xmax)
{
pointf Left[4];
pointf Right[4];
double t;
int no_cross = countHorzCross(pts, ycoord);
if (no_cross == 0)
return -1.0;
/* if 1 crossing and on the line y == ycoord (within 1 point) */
if ((no_cross == 1) && (ROUND(pts[3].y) == ROUND(ycoord))) {
if ((xmin <= pts[3].x) && (pts[3].x <= xmax)) {
return tmax;
} else
return -1.0;
}
/* split the Bezier into halves, trying the first half first. */
Bezier(pts, 3, 0.5, Left, Right);
t = findHorizontal(Left, tmin, (tmin + tmax) / 2.0, ycoord, xmin,
xmax);
if (t >= 0.0)
return t;
return findHorizontal(Right, (tmin + tmax) / 2.0, tmax, ycoord, xmin,
xmax);
}
/* findVertical:
* Given 4 Bezier control points pts, corresponding to the portion
* of an initial spline with path parameter in the range
* 0.0 <= tmin <= t <= tmax <= 1.0, return t where the spline
* first crosses a vertical line segment
* [(xcoord,ymin),(xcoord,ymax)]. Return -1 if not found.
* This is done by binary subdivision.
*/
static double
findVertical(pointf * pts, double tmin, double tmax,
double xcoord, double ymin, double ymax)
{
pointf Left[4];
pointf Right[4];
double t;
int no_cross = countVertCross(pts, xcoord);
if (no_cross == 0)
return -1.0;
/* if 1 crossing and on the line x == xcoord (within 1 point) */
if ((no_cross == 1) && (ROUND(pts[3].x) == ROUND(xcoord))) {
if ((ymin <= pts[3].y) && (pts[3].y <= ymax)) {
return tmax;
} else
return -1.0;
}
/* split the Bezier into halves, trying the first half first. */
Bezier(pts, 3, 0.5, Left, Right);
t = findVertical(Left, tmin, (tmin + tmax) / 2.0, xcoord, ymin, ymax);
if (t >= 0.0)
return t;
return findVertical(Right, (tmin + tmax) / 2.0, tmax, xcoord, ymin,
ymax);
}
inline Coord *Line::clip(Coord *in, const Coord offset, const Region ®, Coord *out) {
double high = 1.0,
low = 0.0;
bool lowInside = reg.Hit(in[0]-offset),
highInside = reg.Hit(in[degree]-offset);
if(lowInside == highInside)
return in;
Coord work[4],
*lowSeg,*highSeg;
if(lowInside) {
lowSeg = 0;
highSeg = work;
}
else {
lowSeg = work;
highSeg = 0;
}
do {
double t = (high + low) / 2.0;
Coord p = Bezier(in,degree,t,lowSeg,highSeg);
bool inside = reg.Hit(p-offset);
if(inside == lowInside)
low = t;
else
high = t;
}
while(high - low > DETAIL); /* should be adaptive with resolution */
for(int i=0;i<=degree;++i)
out[i] = work[i];
return out;
}
static void
gd_bezier(point* A, int n, int arrow_at_start, int arrow_at_end)
{
pointf p0, p1, V[4];
int i, j, step;
int style[20];
int pen, width;
gdImagePtr brush = NULL;
if (cstk[SP].pen != P_NONE) {
if (cstk[SP].pen == P_DASHED) {
for (i = 0; i < 10; i++)
style[i] = cstk[SP].pencolor;
for (; i < 20; i++)
style[i] = gdTransparent;
gdImageSetStyle(im, style, 20);
pen = gdStyled;
} else if (cstk[SP].pen == P_DOTTED) {
for (i = 0; i < 2; i++)
style[i] = cstk[SP].pencolor;
for (; i < 12; i++)
style[i] = gdTransparent;
gdImageSetStyle(im, style, 12);
pen = gdStyled;
} else {
pen = cstk[SP].pencolor;
}
#if 0
if (cstk[SP].penwidth != WIDTH_NORMAL) {
width=cstk[SP].penwidth;
brush = gdImageCreate(width,width);
gdImagePaletteCopy(brush, im);
gdImageFilledRectangle(brush,
0,0,width-1, width-1, cstk[SP].pencolor);
gdImageSetBrush(im, brush);
if (pen == gdStyled) pen = gdStyledBrushed;
else pen = gdBrushed;
}
#else
width = cstk[SP].penwidth;
gdImageSetThickness(im, width);
#endif
V[3].x = A[0].x; V[3].y = A[0].y;
for (i = 0; i+3 < n; i += 3) {
V[0] = V[3];
for (j = 1; j <= 3; j++) {
V[j].x = A[i+j].x; V[j].y = A[i+j].y;
}
p0 = gdpt(V[0]);
for (step = 1; step <= BEZIERSUBDIVISION; step++) {
p1 = gdpt(Bezier(V, 3, (double)step/BEZIERSUBDIVISION, NULL, NULL));
gdImageLine(im, ROUND(p0.x), ROUND(p0.y),
ROUND(p1.x), ROUND(p1.y), pen);
p0 = p1;
}
}
if (brush)
gdImageDestroy(brush);
}
}
pointf dotneato_closest(splines * spl, pointf pt)
{
int i, j, k, besti, bestj;
double bestdist2, d2, dlow2, dhigh2; /* squares of distances */
double low, high, t;
pointf c[4], pt2;
bezier bz;
besti = bestj = -1;
bestdist2 = 1e+38;
for (i = 0; i < spl->size; i++) {
bz = spl->list[i];
for (j = 0; j < bz.size; j++) {
pointf b;
b.x = bz.list[j].x;
b.y = bz.list[j].y;
d2 = DIST2(b, pt);
if ((bestj == -1) || (d2 < bestdist2)) {
besti = i;
bestj = j;
bestdist2 = d2;
}
}
}
bz = spl->list[besti];
/* Pick best Bezier. If bestj is the last point in the B-spline, decrement.
* Then set j to be the first point in the corresponding Bezier by dividing
* then multiplying be 3. Thus, 0,1,2 => 0; 3,4,5 => 3, etc.
*/
if (bestj == bz.size-1)
bestj--;
j = 3*(bestj / 3);
for (k = 0; k < 4; k++) {
c[k].x = bz.list[j + k].x;
c[k].y = bz.list[j + k].y;
}
low = 0.0;
high = 1.0;
dlow2 = DIST2(c[0], pt);
dhigh2 = DIST2(c[3], pt);
do {
t = (low + high) / 2.0;
pt2 = Bezier(c, 3, t, NULL, NULL);
if (fabs(dlow2 - dhigh2) < 1.0)
break;
if (fabs(high - low) < .00001)
break;
if (dlow2 < dhigh2) {
high = t;
dhigh2 = DIST2(pt2, pt);
} else {
low = t;
dlow2 = DIST2(pt2, pt);
}
} while (1);
return pt2;
}
point spline_at_y(splines *spl, int y)
{
int i,j;
double low, high, d, t;
pointf c[4], pt2;
point pt;
static bezier bz;
static splines *mem = NULL;
if (mem != spl) {
mem = spl;
for (i = 0; i < spl->size; i++) {
bz = spl->list[i];
if (BETWEEN (bz.list[bz.size-1].y, y, bz.list[0].y))
break;
}
}
if (y > bz.list[0].y)
pt = bz.list[0];
else if (y < bz.list[bz.size-1].y)
pt = bz.list[bz.size - 1];
else {
for (i = 0; i < bz.size; i += 3) {
for (j = 0; j < 3; j++) {
if ((bz.list[i+j].y <= y) && (y <= bz.list[i+j+1].y))
break;
if ((bz.list[i+j].y >= y) && (y >= bz.list[i+j+1].y))
break;
}
if (j < 3)
break;
}
assert (i < bz.size);
for (j = 0; j < 4; j++) {
c[j].x = bz.list[i + j].x;
c[j].y = bz.list[i + j].y;
/* make the spline be monotonic in Y, awful but it works for now */
if ((j > 0) && (c[j].y > c[j - 1].y))
c[j].y = c[j - 1].y;
}
low = 0.0; high = 1.0;
do {
t = (low + high) / 2.0;
pt2 = Bezier (c, 3, t, NULL, NULL);
d = pt2.y - y;
if (ABS(d) <= 1)
break;
if (d < 0)
high = t;
else
low = t;
} while (1);
pt.x = (int)pt2.x;
pt.y = (int)pt2.y;
}
pt.y = y;
return pt;
}
point dotneato_closest(splines * spl, point p)
{
int i, j, k, besti, bestj;
double bestdist2, d2, dlow2, dhigh2; /* squares of distances */
double low, high, t;
pointf c[4], pt2, pt;
point rv;
bezier bz;
besti = bestj = -1;
bestdist2 = 1e+38;
P2PF(p, pt);
for (i = 0; i < spl->size; i++) {
bz = spl->list[i];
for (j = 0; j < bz.size; j++) {
pointf b;
b.x = bz.list[j].x;
b.y = bz.list[j].y;
d2 = DIST2(b, pt);
if ((bestj == -1) || (d2 < bestdist2)) {
besti = i;
bestj = j;
bestdist2 = d2;
}
}
}
bz = spl->list[besti];
j = bestj / 3;
if (j >= spl->size)
j--;
for (k = 0; k < 4; k++) {
c[k].x = bz.list[j + k].x;
c[k].y = bz.list[j + k].y;
}
low = 0.0;
high = 1.0;
dlow2 = DIST2(c[0], pt);
dhigh2 = DIST2(c[3], pt);
do {
t = (low + high) / 2.0;
pt2 = Bezier(c, 3, t, NULL, NULL);
if (fabs(dlow2 - dhigh2) < 1.0)
break;
if (fabs(high - low) < .00001)
break;
if (dlow2 < dhigh2) {
high = t;
dhigh2 = DIST2(pt2, pt);
} else {
low = t;
dlow2 = DIST2(pt2, pt);
}
} while (1);
PF2P(pt2, rv);
return rv;
}
void VectorFileWriter::BezierAsPwl(SBezier *sb) {
List<Vector> lv;
ZERO(&lv);
sb->MakePwlInto(&lv, SS.ChordTolMm() / SS.exportScale);
int i;
for(i = 1; i < lv.n; i++) {
SBezier sb = SBezier::From(lv.elem[i-1], lv.elem[i]);
Bezier(&sb);
}
lv.Clear();
}
/* splineIntersectf:
* Given four spline control points and a box,
* find the shortest portion of the spline from
* pts[0] to the intersection with the box, if any.
* If an intersection is found, the four points are stored in pts[0..3]
* with pts[3] being on the box, and 1 is returned. Otherwise, pts
* is left unchanged and 0 is returned.
*/
static int splineIntersectf(pointf * pts, boxf * bb)
{
double tmin = 2.0;
double t;
pointf origpts[4];
int i;
for (i = 0; i < 4; i++) {
origpts[i] = pts[i];
}
t = findVertical(pts, 0.0, 1.0, bb->LL.x, bb->LL.y, bb->UR.y);
if ((t >= 0) && (t < tmin)) {
Bezier(origpts, 3, t, pts, NULL);
tmin = t;
}
t = findVertical(pts, 0.0, MIN(1.0, tmin), bb->UR.x, bb->LL.y,
bb->UR.y);
if ((t >= 0) && (t < tmin)) {
Bezier(origpts, 3, t, pts, NULL);
tmin = t;
}
t = findHorizontal(pts, 0.0, MIN(1.0, tmin), bb->LL.y, bb->LL.x,
bb->UR.x);
if ((t >= 0) && (t < tmin)) {
Bezier(origpts, 3, t, pts, NULL);
tmin = t;
}
t = findHorizontal(pts, 0.0, MIN(1.0, tmin), bb->UR.y, bb->LL.x,
bb->UR.x);
if ((t >= 0) && (t < tmin)) {
Bezier(origpts, 3, t, pts, NULL);
tmin = t;
}
if (tmin < 2.0) {
return 1;
} else
return 0;
}
void Bezier(HDC hDC, double x1, double y1, double x2, double y2,
double x3, double y3, double x4, double y4)
{
double A = y4 - y1;
double B = x1 - x4;
double C = y1 * (x4-x1) - x1 * ( y4-y1);
// Ax + By + C = 0 is line (x1,y1) - (x4,y4)
double AB = A * A + B * B;
// distance from (x2,y2) to the line is less than 1
// distance from (x3,y3) to the line is less than 1
if ( ( A * x2 + B * y2 + C ) * ( A * x2 + B * y2 + C ) < AB )
if ( ( A * x3 + B * y3 + C ) * ( A * x3 + B * y3 + C ) < AB )
{
MoveToEx(hDC, (int)x1, (int)y1, NULL);
LineTo(hDC, (int)x4, (int)y4);
return;
}
double x12 = x1+x2;
double y12 = y1+y2;
double x23 = x2+x3;
double y23 = y2+y3;
double x34 = x3+x4;
double y34 = y3+y4;
double x1223 = x12+x23;
double y1223 = y12+y23;
double x2334 = x23+x34;
double y2334 = y23+y34;
double x = x1223 + x2334;
double y = y1223 + y2334;
Bezier(hDC, x1, y1, x12/2, y12/2, x1223/4, y1223/4, x/8, y/8);
Bezier(hDC, x/8, y/8, x2334/4, y2334/4, x34/2, y34/2, x4, y4);
}
int main()
{
int gdriver=DETECT,gmode;
initgraph(&gdriver,&gmode," ");
cleardevice();
int i;
memset(B,0,sizeof(B));//初始化数组全为0
memset(P,0,sizeof(P));
for(i=0;i<sizeof(t)/sizeof(double);i++)
{
B[i][0]=(1-t[i])*(1-t[i])*(1-t[i]);
B[i][1]=3*t[i]*(1-t[i])*(1-t[i]);
B[i][2]=3*t[i]*t[i]*(1-t[i]);
B[i][3]=t[i]*t[i]*t[i];
}
/*for(i=0;i<7;i++)
{
for(j=0;j<4;j++)
{
printf("%f ",B[i][j]);
}
printf("\n");
}*/ //输出B矩阵
Bezier(50,100, 80,230, 100,270 ,140,160);
Bezier(140,160, 180,50, 240,65, 270,120);
Bezier(270,120, 330,230, 380,230, 430,150);
/*for(i=0;i<7;i++)
{
for(j=0;j<2;j++)
{
printf("%f ",P[i][j]);
}
printf("\n");
}*/ //输出P矩阵
getch();
closegraph();
return 0;
}
void Draw_Bezier(float width, float height)
{
float x = width / 2;
float y = height / 2;
Matrix4 t;
t.makeTranslate(-x, -y, 0);
Matrix4 c = objCamera.c;
c = t*c;
c.transpose();
glLoadMatrixd(c.getPointer());
glColor3f(0, 0, 1);
my = Bezier(width, height, angle);
for (float t1 = -0.5; t1 < 0.49; t1 += 0.01)
{
for (float t2 = -0.5; t2 < 0.49; t2 += 0.01)
{
my.tessellate(t1, t2, .1);
}
}
t.makeTranslate(x, -y, 0);
c = objCamera.c;
c = t*c;
c.transpose();
glLoadMatrixd(c.getPointer());
glColor3f(1, 0, 0);
my2 = Bezier(width, height, angle);
for (float t1 = -0.5; t1 < 0.49; t1 += 0.01)
{
for (float t2 = -0.5; t2 < 0.49; t2 += 0.01)
{
my.tessellate(t1, t2, .1);
}
}
}
QImage Polygon::getImage(int width, int height) {
this->width = width;
this->height = height;
lines.clear();
QImage backBuffer(width, height, QImage::Format_RGB888);
backBuffer.fill(qRgb(255, 255, 255));
//drawBezier(&backBuffer, Qt::black);
Bezier(&backBuffer, points[0].x(),points[0].y(), points[1].x(), points[1].y(), points[2].x(), points[2].y(), points[3].x(), points[3].y(), Qt::black);
return backBuffer;
}
point dotneato_closest(splines* spl, point p)
{
int i, j, k, besti, bestj;
double bestdist, d, dlow, dhigh;
double low, high, t;
pointf c[4], pt2, pt;
point rv;
bezier bz;
besti = bestj = -1;
bestdist = 1e+38;
pt.x = p.x; pt.y = p.y;
for (i = 0; i < spl->size; i++) {
bz = spl->list[i];
for (j = 0; j < bz.size; j++) {
pointf b;
b.x = bz.list[j].x; b.y = bz.list[j].y;
d = dist(b,pt);
if ((bestj == -1) || (d < bestdist)) {
besti = i;
bestj = j;
bestdist = d;
}
}
}
bz = spl->list[besti];
j = bestj/3; if (j >= spl->size) j--;
for (k = 0; k < 4; k++) {
c[k].x = bz.list[j + k].x;
c[k].y = bz.list[j + k].y;
}
low = 0.0; high = 1.0;
dlow = dist(c[0],pt);
dhigh = dist(c[3],pt);
do {
t = (low + high) / 2.0;
pt2 = Bezier (c, 3, t, NULL, NULL);
if (fabs(dlow - dhigh) < 1.0) break;
if (low == high) break;
if (dlow < dhigh) {high = t; dhigh = dist(pt2,pt);}
else {low = t; dlow = dist(pt2,pt); }
} while (1);
rv.x = (int)pt2.x;
rv.y = (int)pt2.y;
return rv;
}
static void
vrml_bezier(GVJ_t *job, pointf * A, int n, int arrow_at_start, int arrow_at_end, int filled)
{
obj_state_t *obj = job->obj;
edge_t *e = obj->u.e;
double fstz, sndz;
pointf p1, V[4];
int i, j, step;
assert(e);
fstz = Fstz = obj->tail_z;
sndz = Sndz = obj->head_z;
if (straight(A,n)) {
doSegment (job, A, gvrender_ptf(job, ND_coord(agtail(e))),Fstz,gvrender_ptf(job, ND_coord(aghead(e))),Sndz);
return;
}
gvputs(job, "Shape { geometry Extrusion {\n");
gvputs(job, " spine [");
V[3] = A[0];
for (i = 0; i + 3 < n; i += 3) {
V[0] = V[3];
for (j = 1; j <= 3; j++)
V[j] = A[i + j];
for (step = 0; step <= BEZIERSUBDIVISION; step++) {
p1 = Bezier(V, 3, (double) step / BEZIERSUBDIVISION, NULL, NULL);
gvprintf(job, " %.3f %.3f %.3f", p1.x, p1.y,
interpolate_zcoord(job, p1, A[0], fstz, A[n - 1], sndz));
}
}
gvputs(job, " ]\n");
gvprintf(job, " crossSection [ %.3f %.3f, %.3f %.3f, %.3f %.3f, %.3f %.3f ]\n",
(obj->penwidth), (obj->penwidth), -(obj->penwidth),
(obj->penwidth), -(obj->penwidth), -(obj->penwidth),
(obj->penwidth), -(obj->penwidth));
gvputs(job, "}\n");
gvprintf(job, " appearance DEF E%ld Appearance {\n", AGSEQ(e));
gvputs(job, " material Material {\n");
gvputs(job, " ambientIntensity 0.33\n");
gvprintf(job, " diffuseColor %.3f %.3f %.3f\n",
obj->pencolor.u.rgba[0] / 255.,
obj->pencolor.u.rgba[1] / 255.,
obj->pencolor.u.rgba[2] / 255.);
gvputs(job, " }\n");
gvputs(job, " }\n");
gvputs(job, "}\n");
}
/*
* FindRoots :
* Given a 5th-degree equation in Bernstein-Bezier form, find
* all of the roots in the interval [0, 1]. Return the number
* of roots found.
*/
int Measurement::FindRoots(QPointF* w, int degree,double *t,int depth)
{
int i;
QPointF Left[W_DEGREE+1], /* New left and right */
Right[W_DEGREE+1]; /* control polygons */
int left_count, /* Solution count from */
right_count; /* children */
double left_t[W_DEGREE+1], /* Solutions from kids */
right_t[W_DEGREE+1];
switch (CrossingCount(w, degree)) {
case 0 : { /* No solutions here */
return 0;
}
case 1 : { /* Unique solution */
/* Stop recursion when the tree is deep enough */
/* if deep enough, return 1 solution at midpoint */
if (depth >= MAXDEPTH) {
t[0] = (w[0].rx() + w[W_DEGREE].rx()) / 2.0;
return 1;
}
if (ControlPolygonFlatEnough(w, degree)) {
t[0] = ComputeXIntercept(w, degree);
return 1;
}
break;
}
}
/* Otherwise, solve recursively after */
/* subdividing control polygon */
Bezier(w, degree, 0.5, Left, Right);
left_count = FindRoots(Left, degree, left_t, depth+1);
right_count = FindRoots(Right, degree, right_t, depth+1);
/* Gather solutions together */
for (i = 0; i < left_count; i++) {
t[i] = left_t[i];
}
for (i = 0; i < right_count; i++) {
t[i+left_count] = right_t[i];
}
/* Send back total number of solutions */
return (left_count+right_count);
}
/*
* find_bezier_roots : Given an equation in Bernstein-Bezier form, find all
* of the roots in the interval [0, 1]. Return the number of roots found.
*/
void
find_parametric_bezier_roots(Geom::Point const *w, /* The control points */
unsigned degree, /* The degree of the polynomial */
std::vector<double> &solutions, /* RETURN candidate t-values */
unsigned depth) /* The depth of the recursion */
{
total_steps++;
const unsigned max_crossings = crossing_count(w, degree);
switch (max_crossings) {
case 0: /* No solutions here */
return;
case 1:
/* Unique solution */
/* Stop recursion when the tree is deep enough */
/* if deep enough, return 1 solution at midpoint */
if (depth >= MAXDEPTH) {
solutions.push_back((w[0][Geom::X] + w[degree][Geom::X]) / 2.0);
return;
}
// I thought secant method would be faster here, but it'aint. -- njh
if (control_poly_flat_enough(w, degree)) {
solutions.push_back(compute_x_intercept(w, degree));
return;
}
break;
}
/*
* Otherwise, solve recursively after subdividing control polygon
* New left and right control polygons
*/
Geom::Point *Left = new Geom::Point[degree+1];
Geom::Point *Right = new Geom::Point[degree+1];
Bezier(w, degree, 0.5, Left, Right);
total_subs ++;
find_parametric_bezier_roots(Left, degree, solutions, depth+1);
find_parametric_bezier_roots(Right, degree, solutions, depth+1);
delete[] Left;
delete[] Right;
}
void Shape::addBezier(vector<Point> *result) {
vector<Point> temp;
temp = points;
for(int i=0; i<temp.size(); i++) {
if(temp[i].tag==0) {
vector<Point> control;
vector<Point> bezier;
control.push_back(temp[i]);
i++;
while(i<temp.size() && temp[i].tag==1) {
control.push_back(temp[i]);
i++;
}
if(i>=temp.size()) {
control.push_back(temp[0]);
}
else {
control.push_back(temp[i]);
if(i>=temp.size())
control.push_back(temp[0]);
}
//jika isi control>2, berarti bezier
if(control.size()>2) {
Bezier(control, &bezier);
for(int j=0; j<bezier.size(); j++){
result->push_back(bezier[j]);
}
}
else {
for(int j=0; j<control.size(); j++){
result->push_back(control[j]);
}
}
i--;
}
}
}
void Style::active_bezier() {
if (npara == 3) {
graybg();
int centerx, centery, a = parameters[2];
if (item) {
centerx = item->layer->startx + parameters[0];
centery = item->layer->starty + parameters[1];
}
setcolor(BLACK);
if (item) {
rectangle(item->layer->startx, item->layer->starty, item->layer->endx, item->layer->endy);
}
vector<Point> control;
control.push_back(Point(centerx, item->layer->starty));
control.push_back(Point(item->layer->startx, centery - a / 2));
control.push_back(Point(item->layer->endx, centery + a / 2));
control.push_back(Point(centerx, item->layer->endy));
Bezier(control, BLACK);
}
}
Position Line::Intersection(int seg,Segment other) {
switch(degree) {
case 1:
return lines_intersect(Segment(at(seg),at(seg+1)),other);
case 3:
double roots[4];
/*
if(between(other.a,at(seg),other.b))
return Position(at(seg));
if(between(other.a,at(seg+3),other.b))
return Position(at(seg+3));
*/
if(splineIntersectsLine(&at(seg),other,roots)>0)
return Position(Bezier(&at(seg),3,roots[0]));
else
return Position();
default:
case 0:
return Position();
}
}
void VectorFileWriter::BezierAsNonrationalCubic(SBezier *sb, int depth) {
Vector t0 = sb->TangentAt(0), t1 = sb->TangentAt(1);
// The curve is correct, and the first derivatives are correct, at the
// endpoints.
SBezier bnr = SBezier::From(
sb->Start(),
sb->Start().Plus(t0.ScaledBy(1.0/3)),
sb->Finish().Minus(t1.ScaledBy(1.0/3)),
sb->Finish());
double tol = SS.ChordTolMm() / SS.exportScale;
// Arbitrary choice, but make it a little finer than pwl tolerance since
// it should be easier to achieve that with the smooth curves.
tol /= 2;
bool closeEnough = true;
int i;
for(i = 1; i <= 3; i++) {
double t = i/4.0;
Vector p0 = sb->PointAt(t),
pn = bnr.PointAt(t);
double d = (p0.Minus(pn)).Magnitude();
if(d > tol) {
closeEnough = false;
}
}
if(closeEnough || depth > 3) {
Bezier(&bnr);
} else {
SBezier bef, aft;
sb->SplitAt(0.5, &bef, &aft);
BezierAsNonrationalCubic(&bef, depth+1);
BezierAsNonrationalCubic(&aft, depth+1);
}
}
Position Line::YIntersection(double y) {
if(!size())
return Position();
for(unsigned i = 0; i < size(); i += degree)
if(at(i).y == y)
return Position(at(i));
int seg = GetSeg(y);
if(seg < 0)
return Position();
double high,low;
if(at(seg).y < at(seg+degree).y) {
high = 1.0;
low = 0.0;
}
else {
high = 0.0;
low = 1.0;
}
double close = DBL_MAX;
Coord ret;
do {
double t = (high + low) / 2.0;
Coord p = Bezier(&at(seg),degree,t);
double d = absol(p.y - y);
if(d < close) {
ret = p;
close = d;
}
if(p.y > y)
high = t;
else
low = t;
}
while(absol(high - low) > .01); /* should be adaptive */
return Position(ret);
}
void Style::normal_bezier() {
if (npara == 3) {
setlinestyle(SOLID_LINE, 0, NORM_WIDTH);
setfillstyle(SOLID_FILL, WHITE);
if (item) {
bar(item->layer->startx + 1, item->layer->starty + 1, item->layer->endx, item->layer->endy);
}
int centerx, centery, a = parameters[2];
if (item) {
centerx = item->layer->startx + parameters[0];
centery = item->layer->starty + parameters[1];
}
setcolor(BLACK);
if (item) {
rectangle(item->layer->startx, item->layer->starty, item->layer->endx, item->layer->endy);
}
vector<Point> control;
control.push_back(Point(centerx, item->layer->starty));
control.push_back(Point(item->layer->startx, centery - a / 2));
control.push_back(Point(item->layer->endx, centery + a / 2));
control.push_back(Point(centerx, item->layer->endy));
Bezier(control, BLACK);
}
}
//Display
void display (void)
{
glClearColor(rosso_sf,verde_sf,blu_sf,0.0);//rendo variabili i parametri che mi definiscono il colore
glClear(GL_COLOR_BUFFER_BIT);
int i;
glColor3f(0.0,0.0,1.0);
glPointSize(dimpunto);
glBegin(GL_POINTS);//per visualizzare anche i punti dove si clicca di colore blu
for (i=1;i<=last;i++)
glVertex2f(Punti[i].x,Punti[i].y);
glEnd();
glColor3f(rosso_dis,verde_dis,blu_dis);
glBegin(GL_LINE_STRIP); //poligono di controllo
for (i=1;i<=last;i++)
glVertex2f(Punti[i].x,Punti[i].y);
glEnd();
n=last;//setto n al numero di punti disegnato
for(i=1;i<=n;i++)
w[i]=1;//metto tutti i pesi a 1
//scelta parametrizzazione
if (scelta_param==0)
{
Parametrizzazione_Uniforme();
}
else if(scelta_param==1)
{
Parametrizzazione_Corde();
}
//scelta della funzione
glPointSize(2);//la curva la disegno sempre di dimensione 2
if (metodo=='H' && last>1)
{
Hermite();
Disegna_Funzioni_Base();
}
if (metodo=='B' && last>1)
{
if(mod_pesi_bez==1)
w[i_p_b]=val_peso;
Bezier();
if (subd==1)
Subdivision();
if (d_el==1)
Degree_Elevation();
Disegna_fBaseBernstein();
}
if (metodo=='S' && last>3)
{
if(mod_pesi_spline==1)
w[i_p_s]=val_pesos;
Costruisci_Nodi();
Funzioni_Bspline(Nodi);
De_Boor();
}
//glutPostRedisplay();//è per questo che le funzioni base saltellano :)...se non lo metti però quando cambi il metodo non viene cambiato immediatamente ma dopo aver spinto un altro punto
glFlush();
}