Abstract: A recently rendered section of a curve is redrawn to smooth the curve on-the-fly while a user moves a stylus or other input device. On receiving data points for the curve, an old rendered section for prior data points is deleted by curve redrawing code, and a new spline that's visually smooth through the new data points and at least one prior data point is added. “Visually smooth” is defined using tangents. The rendered spline is a cardinal or other cubic Hermite spline. The curve is redrawn for display by overwriting frame buffer data. A single instruction multiple data processing architecture simultaneously calculates multiple data points for the new section of the curve rendering. A digital ink rendering uses a pen-tip shape or an arc shape, based on data point locations. The pen-tip shape simulates a square-tip pen, highlighter, pencil, charcoal, paintbrush, or liquid ink pen.

Abstract: With some splines, such as cardinal splines, irregularly spaced data points may cause undesired bumps. Bump moderation makes a spline curve more visually appealing by reducing bumps, and by doing so even if the curve happens to be already smooth in a mathematical sense. Data points P1, P2, and P3 are not suitably spaced an outlier is present in a set of linear distances between the points. The bump is moderated by moving a point of the spline along a pathway to a position for which the data points P1, P2, and P3 are suitably spaced. The pathway may be a Bezier segment or a line segment. A point is moved on the pathway to its midpoint, or to a particular portion of the pathway such as its central third or central fifth.

Abstract: A recently rendered section of a curve is redrawn to smooth the curve on-the-fly while a user moves a stylus or other input device. On receiving data points for the curve, an old rendered section for prior data points is deleted by curve redrawing code, and a new spline that's visually smooth through the new data points and at least one prior data point is added. “Visually smooth” is defined using tangents. The rendered spline is a cardinal or other cubic Hermite spline. The curve is redrawn for display by overwriting frame buffer data. A single instruction multiple data processing architecture simultaneously calculates multiple data points for the new section of the curve rendering. A digital ink rendering uses a pen-tip shape or an arc shape, based on data point locations. The pen-tip shape simulates a square-tip pen, highlighter, pencil, charcoal, paintbrush, or liquid ink pen.

Abstract: A recently rendered section of a curve is redrawn to smooth the curve on-the-fly while a user moves a stylus or other input device. On receiving data points for the curve, an old rendered section for prior data points is deleted by curve redrawing code, and a new spline that's visually smooth through the new data points and at least one prior data point is added. “Visually smooth” is defined using tangents. The rendered spline is a cardinal or other cubic Hermite spline. The curve is redrawn for display by overwriting frame buffer data. A single instruction multiple data processing architecture simultaneously calculates multiple data points for the new section of the curve rendering. A digital ink rendering uses a pen-tip shape or an arc shape, based on data point locations. The pen-tip shape simulates a square-tip pen, highlighter, pencil, charcoal, paintbrush, or liquid ink pen.

Abstract: With some splines, such as cardinal splines, irregularly spaced data points may cause undesired bumps. Bump moderation makes a spline curve more visually appealing by reducing bumps, and by doing so even if the curve happens to be already smooth in a mathematical sense. Data points P1, P2, and P3 are not suitably spaced an outlier is present in a set of linear distances between the points. The bump is moderated by moving a point of the spline along a pathway to a position for which the data points P1, P2, and P3 are suitably spaced. The pathway may be a Bezier segment or a line segment. A point is moved on the pathway to its midpoint, or to a particular portion of the pathway such as its central third or central fifth.

Abstract: With some splines, such as cardinal splines, irregularly spaced data points may cause undesired bumps. Bump moderation makes a spline curve more visually appealing by reducing bumps, and by doing so even if the curve happens to be already smooth in a mathematical sense. Data points P1, P2, and P3 are not suitably spaced an outlier is present in a set of linear distances between the points. The bump is moderated by moving a point of the spline along a pathway to a position for which the data points P1, P2, and P3 are suitably spaced. The pathway may be a Bezier segment or a line segment. A point is moved on the pathway to its midpoint, or to a particular portion of the pathway such as its central third or central fifth.

Abstract: A display application rotates content to provide a perspective view along the z-axis during a scroll action as a feedback to a user indicating a scroll action has reached a beginning or an end of available content. Determined direction and speed and/or acceleration of the scroll action is applied to move content and rotate it based on: a tilt angle proportional to the speed and/or acceleration and a rotation axis perpendicular to the direction. Additional content is displayed in the perspective view based on the tilt angle. And, the tilt angle is adjusted to rotate the content in response to reaching an end of the content during the scroll action or upon detecting a subsequent scroll action.

Abstract: A display application rotates content to provide a perspective view along the z-axis during a scroll action as a feedback to a user indicating a scroll action has reached a beginning or an end of available content. Determined direction and speed and/or acceleration of the scroll action is applied to move content and rotate it based on: a tilt angle proportional to the speed and/or acceleration and a rotation axis perpendicular to the direction. Additional content is displayed in the perspective view based on the tilt angle. And, the tilt angle is adjusted to rotate the content in response to reaching an end of the content during the scroll action or upon detecting a subsequent scroll action.

Abstract: With some splines, such as cardinal splines, irregularly spaced data points may cause undesired bumps. Bump moderation makes a spline curve more visually appealing by reducing bumps, and by doing so even if the curve happens to be already smooth in a mathematical sense. Data points P1, P2, and P3 are not suitably spaced an outlier is present in a set of linear distances between the points. The bump is moderated by moving a point of the spline along a pathway to a position for which the data points P1, P2, and P3 are suitably spaced. The pathway may be a Bezier segment or a line segment. A point is moved on the pathway to its midpoint, or to a particular portion of the pathway such as its central third or central fifth.

Abstract: A recently rendered section of a curve is redrawn to smooth the curve on-the-fly while a user moves a stylus or other input device. On receiving data points for the curve, an old rendered section for prior data points is deleted by curve redrawing code, and a new spline that's visually smooth through the new data points and at least one prior data point is added. “Visually smooth” is defined using tangents. The rendered spline is a cardinal or other cubic Hermite spline. The curve is redrawn for display by overwriting frame buffer data. A single instruction multiple data processing architecture simultaneously calculates multiple data points for the new section of the curve rendering. A digital ink rendering uses a pen-tip shape or an arc shape, based on data point locations. The pen-tip shape simulates a square-tip pen, highlighter, pencil, charcoal, paintbrush, or liquid ink pen.