API
ptn_functions.geo
The ptn_functions.geo file contains various functions to solve for geometrical problems. All functions are designed for 2D space, i.e. the z-coordinate is ignored, unless otherwise stated.
calc_intersection_line_circle
Description
Calculates the x and y coordinates of a point on the intersection between a line and a circle. Returns x and y coordinates of the point of the intersection.
Parameters
| Name | Description | Default |
|---|---|---|
ptn_p1 and ptn_p2 |
Endpoints of a line. | required |
ptn_p3 |
Point at center of circle. | required |
ptn_circ_rad |
Radius of circle. | required |
Returns
There are two solutions for the intersection between a line and a circle.
| Name | Description |
|---|---|
ptn_inter1_x |
X-coordinate of first solution. |
ptn_inter1_y |
Y-coordinate of first solution. |
ptn_inter2_x |
X-coordinate of second solution. |
ptn_inter2_y |
Y-coordinate of second solution. |
calc_intersection_of_two_arcs
Description
Calculates the x and y coordinates of a point on the intersection between two arcs or circles of the same radius.
Parameters
| Name | Description | Default |
|---|---|---|
ptn_p1 |
Point at center of first circle. | required |
ptn_p2 |
Point at center of second circle. | required |
ptn_circ_rad_1 |
Radius of first circle. | required |
ptn_circ_rad_2 |
Radius of second circle. | required |
Returns
The function returns two solutions for intersection between two arcs or circles.
| Name | Description |
|---|---|
ptn_inter1_x |
X-coordinate of first solution. |
ptn_inter1_y |
Y-coordinate of first solution. |
ptn_inter2_x |
X-coordinate of second solution. |
ptn_inter2_y |
Y-coordinate of second solution. |
calc_angle_btw_two_vectors
Description
Calculates angle between two vectors / lines with originate at the same point. Returns angle in radians.
Parameters
| Name | Description | Default |
|---|---|---|
ptn_p1 |
Origin of both vectors / lines. | required |
ptn_p2 |
Endpoint of first line.. | required |
ptn_p3 |
Endpoint of second line. | required |
Returns
The function returns the intersection between two arcs or circles.
| Name | Description |
|---|---|
ptn_anglex |
Angle between two vectors in radians. |
calc_intersection_btw_two_lines
Description
Calculates the x and y coordinates of a point on the intersection between two lines.
Parameters
| Name | Description | Default |
|---|---|---|
ptn_p1 and ptn_p2 |
Endpoints of first line. | required |
ptn_p3 and ptn_p4 |
Endpoints of second line. | required |
Returns
Returns intersection between two lines.
| Name | Description |
|---|---|
ptn_inter_x |
X-coordinate of intersetion. |
ptn_inter_y |
Y-coordinate of intersetion. |
calc_distance_btw_two_points
Description
Calculates the distance between two points. Works in 3D space.
Parameters
| Name | Description | Default |
|---|---|---|
ptn_p1 |
Point in 3D space. | required |
ptn_p2 |
Point in 3D space. | required |
Returns
Returns shortest distance between two points.
| Name | Description |
|---|---|
ptn_dist |
Distance between two points. |
ptn_bezier_functions.geo
slice_bezier_param
Description
Slices a cubic Bezier curve into two cubic Bezier curves. Endpoints are startpoint (ptn_p1) of first Bezier curve and endpoint (ptn_p4) of second Bezier curve.
Parameters
| Name | Description | Default |
|---|---|---|
ptn_param |
Ratio at which curve is split. | required |
ptn_p1 |
End point of Bezier curve. | required |
ptn_p2 |
Control point of Bezier curve. | required |
ptn_p3 |
Control point of Bezier curve. | required |
ptn_p4 |
End point of Bezier curve. | required |
Returns
| Name | Description |
|---|---|
x12 and y12 |
Coordinates of control point for first new curve. |
x123 and y123 |
Coordinates of control point for first new curve. |
x1234 and y1234 |
Coordinates of splitting point. End point for both new bezier curves. |
x234 and y234 |
Coordinates of control point for second new curve. |
x34 and y34 |
Coordinates of control point for second new curve. |
calc_intersection_Bezier_line
Description
Calculates the intersection between a Bezier curve and a line by using the Newton's method.
Parameters
| Name | Description | Default |
|---|---|---|
ptn_p1 |
End point of Bezier curve. | required |
ptn_p2 |
Control point of Bezier curve. | required |
ptn_p3 |
Control point of Bezier curve. | required |
ptn_p4 |
End point of Bezier curve. | required |
ptn_pline1 and ptn_pline2 |
End points of line. | required |
Returns
Calculates parameter, i.e. ratio at which Bezier needs to be split. Necessary as input for slice_bezier_param.
| Name | Description |
|---|---|
ptn_param |
Ratio at which curve is split for intersection. |
Example
Slice circlular arc of radius 1 centered at origin (0,0) with a horizontal line at y=0.5.
Include "ptn_bezier_functions.geo";
k=0.5522847498;
Point(1) = {0, 1, 0};
Point(2) = {k, 1, 0};
Point(3) = {1, k, 0};
Point(4) = {1, 0, 0};
ptn_p1[] = Point{1};
ptn_p2[] = Point{2};
ptn_p3[] = Point{3};
ptn_p4[] = Point{4};
ptn_pline1[] = {0., 0.5, 0.}; // start point line
ptn_pline2[] = {10., 0.5, 0.}; // end point line
Call calc_intersection_Bezier_line;
Call slice_bezier_param;
Point(1002) = {ptn_x12, ptn_y12, 0}; // Control point
Point(1003) = {ptn_x123, ptn_y123, 0}; // Control point
Point(1004) = {ptn_x1234, ptn_y1234, 0}; // Intersecting
Point(1005) = {ptn_x234, ptn_y234, 0}; // Control point
Point(1006) = {ptn_x34, ptn_y34, 0}; // Control point
Bezier(101) = {1, 1002, 1003, 1004};
Bezier(102) = {1004, 1005, 1006, 4};