fastwater.otm_gpl.geometry module

@note … this work is based on a collaborative effort of the Telemac-Mascaret consortium

@history 11/11/2011 – Sebastien E. Bourban

An accuracy has been introduced because Python does not seem to be accurate with sums and multiplications

@history 07/12/2011 – Sebastien E. Bourban

Addition of 3 new geometrical tools: + get_segment_line_intersection (different from

get_segment_intersection)

• get_plane_equation (of the form Z = a*X + b*Y + c)

• get_triangle_area

@history 07/01/2012 – Sebastien E. Bourban

Addition of a few geometrical tools, working on angles: + get_cone_angle ( based on arctan2 ) + get_cone_sin_angle ( S = ac.sin(B)/2 = det / 2 )

@history 14/02/2012 – Sebastien E. Bourban, Laure C. Grignon

Addition of the is_inside_poly method to define whether a point is inside of a polygon based on the ray casting method

@brief

Tools for trivial geometrical operations

fastwater.otm_gpl.geometry.get_barycentric_weights(point_0, point_1, point_2, point_3)

Returns the barycentric weights of point point_0 in regard to the three points (point_1, point_2, point_3)

@param point_0 (2-uple) Coordinates of the point for which we want the weight @param point_1 (2-uple) Coodiantes of the first of the three points @param point_2 (2-uple) Coodiantes of the second of the three points @param point_3 (2-uple) Coodiantes of the third of the three points

@returns (3-uple) weight in regard of each point

fastwater.otm_gpl.geometry.get_cone_angle(t_1, t_2, t_3)

fastwater.otm_gpl.geometry.get_cone_sin_angle(t_1, t_2, t_3)

fastwater.otm_gpl.geometry.get_distance_point_to_line(point_0, point_1, point_2)

Returns the distance between a point and a line

@param point_0 (2-uple) Coodinates of the point @param point_1 (2-uple) Coodinates of the first point of the line @param point_2 (2-uple) Coodinates of the second point of the line

@returns (float) the distance

fastwater.otm_gpl.geometry.get_norm2(point1, point2)

Compute norm2 of points given in argument: sqrt((y_2-y_1)^2+(x_2-x_1)^2)

@param point1 (2-uple) Coordinates of the point (x1, y1) @param point2 (2-uple) Coordinates of the point (x2, y2)

@returns (float) The norm

fastwater.otm_gpl.geometry.get_plane_equation(point_1, point_2, point_3)

Find the equation of the plane defined by 3 points. The form of the equation is: Z = a*X + b*Y + c

@param point_1 (2-uple) coordiantes of the first point @param point_2 (2-uple) coordiantes of the second point @param point_3 (2-uple) coordiantes of the third point

@returns (3-uple) (a, b, c)

fastwater.otm_gpl.geometry.get_segment_intersection(point_1, point_2, point_3, point_4)

Returns the coordinate of the point at the intersection of two segments, defined by (point_1,point_2) and (point_3,point_4) and ratio (exaplined below)

@param point_1 (2-uple) first point of the first segment @param point_2 (2-uple) second point of the first segment @param point_3 (2-uple) first point of the second segment @param point_4 (2-uple) second point of the second segment

@return [[x0,y0], ratio] where x0 and y0 are the coordinates of the intersect point and ratio that is norm2(point0, point1)/norm2(point1, point2)

fastwater.otm_gpl.geometry.get_segment_line_intersection(t_1, t_2, t_3, t_4)

@brief Returns the coordinate of the point at the intersection

of one segments defined by (p_1,p_2) and one line (p_3,p_4)

fastwater.otm_gpl.geometry.get_triangle_area(point_1, point_2, point_3)

Compute the area of a triangle

@param point_1 (2-uple) Coordinates of the first point of the triangle @param point_2 (2-uple) Coordinates of the second point of the triangle @param point_3 (2-uple) Coordinates of the third point of the triangle

@returns The area

fastwater.otm_gpl.geometry.is_ccw(t_1, t_2, t_3)

@brief Checks if the element is conterclockwise oriented or not

@param t_1 (tuple): coordinates of node 1 @param t_2 (tuple): coordinates of node 2 @param t_3 (tuple): coordinates of node 3

@return True if it is oriented counterclockwise, False otherwise

fastwater.otm_gpl.geometry.is_close(p_1, p_2, size=5)

Checks if two points are near each other

@param p_1 (2-uple) Coordianate of the first point @param p_2 (2-uple) Coordianate of the second point @param size (int) Additional offset for accuracy (10^-size)

fastwater.otm_gpl.geometry.is_inside_poly(t_o, poly, close=True)

Check if a point is in a polygon using Ray Casting Method

@param t_o (2-uple) Coordinates of the point @param poly (list) list of point of the polygon @param close (boolean) if true also check if the point is near the boundary of the polygon

@returns (boolean) True if inside

fastwater.otm_gpl.geometry.is_inside_triangle(t_o, t_1, t_2, t_3, size=5, nomatter=False)