tktrig.c

linux系统下的音频通信

	    } else {
		y = MIN(pPtr[3], pointPtr[1]);
		y = MAX(y, pPtr[1]);
	    }
	} else if (pPtr[3] == pPtr[1]) {

	    /*
	     * Horizontal edge.
	     */

	    y = pPtr[1];
	    if (pPtr[0] >= pPtr[2]) {
		x = MIN(pPtr[0], pointPtr[0]);
		x = MAX(x, pPtr[2]);
		if ((pointPtr[1] < y) && (pointPtr[0] < pPtr[0])
			&& (pointPtr[0] >= pPtr[2])) {
		    intersections++;
		}
	    } else {
		x = MIN(pPtr[2], pointPtr[0]);
		x = MAX(x, pPtr[0]);
		if ((pointPtr[1] < y) && (pointPtr[0] < pPtr[2])
			&& (pointPtr[0] >= pPtr[0])) {
		    intersections++;
		}
	    }
	} else {
	    double m1, b1, m2, b2;
	    int lower;			/* Non-zero means point below line. */

	    /*
	     * The edge is neither horizontal nor vertical.  Convert the
	     * edge to a line equation of the form y = m1*x + b1.  Then
	     * compute a line perpendicular to this edge but passing
	     * through the point, also in the form y = m2*x + b2.
	     */

	    m1 = (pPtr[3] - pPtr[1])/(pPtr[2] - pPtr[0]);
	    b1 = pPtr[1] - m1*pPtr[0];
	    m2 = -1.0/m1;
	    b2 = pointPtr[1] - m2*pointPtr[0];
	    x = (b2 - b1)/(m1 - m2);
	    y = m1*x + b1;
	    if (pPtr[0] > pPtr[2]) {
		if (x > pPtr[0]) {
		    x = pPtr[0];
		    y = pPtr[1];
		} else if (x < pPtr[2]) {
		    x = pPtr[2];
		    y = pPtr[3];
		}
	    } else {
		if (x > pPtr[2]) {
		    x = pPtr[2];
		    y = pPtr[3];
		} else if (x < pPtr[0]) {
		    x = pPtr[0];
		    y = pPtr[1];
		}
	    }
	    lower = (m1*pointPtr[0] + b1) > pointPtr[1];
	    if (lower && (pointPtr[0] >= MIN(pPtr[0], pPtr[2]))
		    && (pointPtr[0] < MAX(pPtr[0], pPtr[2]))) {
		intersections++;
	    }
	}

	/*
	 * Compute the distance to the closest point, and see if that
	 * is the best distance seen so far.
	 */

	dist = hypot(pointPtr[0] - x, pointPtr[1] - y);
	if (dist < bestDist) {
	    bestDist = dist;
	}
    }

    /*
     * We've processed all of the points.  If the number of intersections
     * is odd, the point is inside the polygon.
     */

    if (intersections & 0x1) {
	return 0.0;
    }
    return bestDist;
}

/*
 *--------------------------------------------------------------
 *
 * TkPolygonToArea --
 *
 *	Determine whether a polygon lies entirely inside, entirely
 *	outside, or overlapping a given rectangular area.
 *
 * Results:
 *	-1 is returned if the polygon given by polyPtr and numPoints
 *	is entirely outside the rectangle given by rectPtr.  0 is
 *	returned if the polygon overlaps the rectangle, and 1 is
 *	returned if the polygon is entirely inside the rectangle.
 *
 * Side effects:
 *	None.
 *
 *--------------------------------------------------------------
 */

int
TkPolygonToArea(polyPtr, numPoints, rectPtr)
    double *polyPtr;		/* Points to an array coordinates for
				 * closed polygon:  x0, y0, x1, y1, ...
				 * The polygon may be self-intersecting. */
    int numPoints;		/* Total number of points at *polyPtr. */
    register double *rectPtr;	/* Points to coords for rectangle, in the
				 * order x1, y1, x2, y2.  X1 and y1 must
				 * be lower-left corner. */
{
    int state;			/* State of all edges seen so far (-1 means
				 * outside, 1 means inside, won't ever be
				 * 0). */
    int count;
    register double *pPtr;

    /*
     * Iterate over all of the edges of the polygon and test them
     * against the rectangle.  Can quit as soon as the state becomes
     * "intersecting".
     */

    state = TkLineToArea(polyPtr, polyPtr+2, rectPtr);
    if (state == 0) {
	return 0;
    }
    for (pPtr = polyPtr+2, count = numPoints-1; count >= 2;
	    pPtr += 2, count--) {
	if (TkLineToArea(pPtr, pPtr+2, rectPtr) != state) {
	    return 0;
	}
    }

    /*
     * If all of the edges were inside the rectangle we're done.
     * If all of the edges were outside, then the rectangle could
     * still intersect the polygon (if it's entirely enclosed).
     * Call TkPolygonToPoint to figure this out.
     */

    if (state == 1) {
	return 1;
    }
    if (TkPolygonToPoint(polyPtr, numPoints, rectPtr) == 0.0) {
	return 0;
    }
    return -1;
}

/*
 *--------------------------------------------------------------
 *
 * TkOvalToPoint --
 *
 *	Computes the distance from a given point to a given
 *	oval, in canvas units.
 *
 * Results:
 *	The return value is 0 if the point given by *pointPtr is
 *	inside the oval.  If the point isn't inside the
 *	oval then the return value is approximately the distance
 *	from the point to the oval.  If the oval is filled, then
 *	anywhere in the interior is considered "inside";  if
 *	the oval isn't filled, then "inside" means only the area
 *	occupied by the outline.
 *
 * Side effects:
 *	None.
 *
 *--------------------------------------------------------------
 */

	/* ARGSUSED */
double
TkOvalToPoint(ovalPtr, width, filled, pointPtr)
    double ovalPtr[4];		/* Pointer to array of four coordinates
				 * (x1, y1, x2, y2) defining oval's bounding
				 * box. */
    double width;		/* Width of outline for oval. */
    int filled;			/* Non-zero means oval should be treated as
				 * filled;  zero means only consider outline. */
    double pointPtr[2];		/* Coordinates of point. */
{
    double xDelta, yDelta, scaledDistance, distToOutline, distToCenter;
    double xDiam, yDiam;

    /*
     * Compute the distance between the center of the oval and the
     * point in question, using a coordinate system where the oval
     * has been transformed to a circle with unit radius.
     */

    xDelta = (pointPtr[0] - (ovalPtr[0] + ovalPtr[2])/2.0);
    yDelta = (pointPtr[1] - (ovalPtr[1] + ovalPtr[3])/2.0);
    distToCenter = hypot(xDelta, yDelta);
    scaledDistance = hypot(xDelta / ((ovalPtr[2] + width - ovalPtr[0])/2.0),
	    yDelta / ((ovalPtr[3] + width - ovalPtr[1])/2.0));


    /*
     * If the scaled distance is greater than 1 then it means no
     * hit.  Compute the distance from the point to the edge of
     * the circle, then scale this distance back to the original
     * coordinate system.
     *
     * Note: this distance isn't completely accurate.  It's only
     * an approximation, and it can overestimate the correct
     * distance when the oval is eccentric.
     */

    if (scaledDistance > 1.0) {
	return (distToCenter/scaledDistance) * (scaledDistance - 1.0);
    }

    /*
     * Scaled distance less than 1 means the point is inside the
     * outer edge of the oval.  If this is a filled oval, then we
     * have a hit.  Otherwise, do the same computation as above
     * (scale back to original coordinate system), but also check
     * to see if the point is within the width of the outline.
     */

    if (filled) {
	return 0.0;
    }
    if (scaledDistance > 1E-10) {
	distToOutline = (distToCenter/scaledDistance) * (1.0 - scaledDistance)
		- width;
    } else {
	/*
	 * Avoid dividing by a very small number (it could cause an
	 * arithmetic overflow).  This problem occurs if the point is
	 * very close to the center of the oval.
	 */

	xDiam = ovalPtr[2] - ovalPtr[0];
	yDiam = ovalPtr[3] - ovalPtr[1];
	if (xDiam < yDiam) {
	    distToOutline = (xDiam - width)/2;
	} else {
	    distToOutline = (yDiam - width)/2;
	}
    }

    if (distToOutline < 0.0) {
	return 0.0;
    }
    return distToOutline;
}

/*
 *--------------------------------------------------------------
 *
 * TkOvalToArea --
 *
 *	Determine whether an oval lies entirely inside, entirely
 *	outside, or overlapping a given rectangular area.
 *
 * Results:
 *	-1 is returned if the oval described by ovalPtr is entirely
 *	outside the rectangle given by rectPtr.  0 is returned if the
 *	oval overlaps the rectangle, and 1 is returned if the oval
 *	is entirely inside the rectangle.
 *
 * Side effects:
 *	None.
 *
 *--------------------------------------------------------------
 */

int
TkOvalToArea(ovalPtr, rectPtr)
    register double *ovalPtr;	/* Points to coordinates definining the
				 * bounding rectangle for the oval: x1, y1,
				 * x2, y2.  X1 must be less than x2 and y1
				 * less than y2. */
    register double *rectPtr;	/* Points to coords for rectangle, in the
				 * order x1, y1, x2, y2.  X1 and y1 must
				 * be lower-left corner. */
{
    double centerX, centerY, radX, radY, deltaX, deltaY;

    /*
     * First, see if oval is entirely inside rectangle or entirely
     * outside rectangle.
     */

    if ((rectPtr[0] <= ovalPtr[0]) && (rectPtr[2] >= ovalPtr[2])
	    && (rectPtr[1] <= ovalPtr[1]) && (rectPtr[3] >= ovalPtr[3])) {
	return 1;
    }
    if ((rectPtr[2] < ovalPtr[0]) || (rectPtr[0] > ovalPtr[2])
	    || (rectPtr[3] < ovalPtr[1]) || (rectPtr[1] > ovalPtr[3])) {
	return -1;
    }

    /*
     * Next, go through the rectangle side by side.  For each side
     * of the rectangle, find the point on the side that is closest
     * to the oval's center, and see if that point is inside the
     * oval.  If at least one such point is inside the oval, then
     * the rectangle intersects the oval.
     */

    centerX = (ovalPtr[0] + ovalPtr[2])/2;
    centerY = (ovalPtr[1] + ovalPtr[3])/2;
    radX = (ovalPtr[2] - ovalPtr[0])/2;
    radY = (ovalPtr[3] - ovalPtr[1])/2;

    deltaY = rectPtr[1] - centerY;
    if (deltaY < 0.0) {
	deltaY = centerY - rectPtr[3];
	if (deltaY < 0.0) {
	    deltaY = 0;
	}
    }
    deltaY /= radY;
    deltaY *= deltaY;

    /*
     * Left side:
     */

    deltaX = (rectPtr[0] - centerX)/radX;
    deltaX *= deltaX;
    if ((deltaX + deltaY) <= 1.0) {
	return 0;
    }

    /*
     * Right side:
     */

    deltaX = (rectPtr[2] - centerX)/radX;
    deltaX *= deltaX;
    if ((deltaX + deltaY) <= 1.0) {
	return 0;
    }

    deltaX = rectPtr[0] - centerX;
    if (deltaX < 0.0) {
	deltaX = centerX - rectPtr[2];
	if (deltaX < 0.0) {
	    deltaX = 0;
	}
    }
    deltaX /= radX;
    deltaX *= deltaX;

    /*
     * Bottom side:
     */

    deltaY = (rectPtr[1] - centerY)/radY;
    deltaY *= deltaY;
    if ((deltaX + deltaY) < 1.0) {
	return 0;
    }

    /*
     * Top side:
     */

    deltaY = (rectPtr[3] - centerY)/radY;
    deltaY *= deltaY;
    if ((deltaX + deltaY) < 1.0) {
	return 0;
    }

    return -1;
}

/*
 *--------------------------------------------------------------
 *
 * TkIncludePoint --
 *
 *	Given a point and a generic canvas item header, expand
 *	the item's bounding box if needed to include the point.
 *
 * Results:
 *	None.
 *
 * Side effects:
 *	The boudn.
 *
 *--------------------------------------------------------------
 */

	/* ARGSUSED */
void
TkIncludePoint(itemPtr, pointPtr)
    register Tk_Item *itemPtr;		/* Item whose bounding box is
					 * being calculated. */
    double *pointPtr;			/* Address of two doubles giving
					 * x and y coordinates of point. */
{
    int tmp;

    tmp = (int) (pointPtr[0] + 0.5);
    if (tmp < itemPtr->x1) {
	itemPtr->x1 = tmp;
    }
    if (tmp > itemPtr->x2) {
	itemPtr->x2 = tmp;
    }
    tmp = (int) (pointPtr[1] + 0.5);
    if (tmp < itemPtr->y1) {
	itemPtr->y1 = tmp;
    }
    if (tmp > itemPtr->y2) {
	itemPtr->y2 = tmp;
    }
}

/*
 *--------------------------------------------------------------
 *
 * TkBezierScreenPoints --
 *
 *	Given four control points, create a larger set of XPoints
 *	for a Bezier spline based on the points.
 *
 * Results:
 *	The array at *xPointPtr gets filled in with numSteps XPoints
 *	corresponding to the Bezier spline defined by the four 
 *	control points.  Note:  no output point is generated for the
 *	first input point, but an output point *is* generated for
 *	the last input point.
 *
 * Side effects:
 *	None.
 *
 *--------------------------------------------------------------
 */

void
TkBezierScreenPoints(canvas, control, numSteps, xPointPtr)
    Tk_Canvas canvas;			/* Canvas in which curve is to be
					 * drawn. */
    double control[];			/* Array of coordinates for four
					 * control points:  x0, y0, x1, y1,
					 * ... x3 y3. */
    int numSteps;			/* Number of curve points to
					 * generate.  */
    register XPoint *xPointPtr;		/* Where to put new points. */
{
    int i;
    double u, u2, u3, t, t2, t3;

    for (i = 1; i <= numSteps; i++, xPointPtr++) {
	t = ((double) i)/((double) numSteps);
	t2 = t*t;
	t3 = t2*t;
	u = 1.0 - t;
	u2 = u*u;
	u3 = u2*u;
	Tk_CanvasDrawableCoords(canvas,
		(control[0]*u3 + 3.0 * (control[2]*t*u2 + control[4]*t2*u)
		    + control[6]*t3),
		(control[1]*u3 + 3.0 * (control[3]*t*u2 + control[5]*t2*u)
		    + control[7]*t3),
		&xPointPtr->x, &xPointPtr->y);
    }
}

/*
 *--------------------------------------------------------------
 *
 * TkBezierPoints --
 *
 *	Given four control points, create a larger set of points
 *	for a Bezier spline based on the points.
 *
 * Results:
 *	The array at *coordPtr gets filled in with 2*numSteps
 *	coordinates, which correspond to the Bezier spline defined
 *	by the four control points.  Note:  no output point is
 *	generated for the first input point, but an output point
 *	*is* generated for the last input point.
 *