#!/usr/bin/python
# -*- coding: windows-1251 -*-

#
# Visualization of a Hermite spline.
#
# Used to evaluate how much differs a two-interpolated-coordinates spline
# from a single-interpolated-coordinate variant (which is used to interpolate
# lens model terms).
#

from sys import *;
from time import *;
from pygame import *;

TENSION = 0.5 # 0..1

def spline(P1, P2, P3, P4, t):
    t2 = t * t;
    t3 = t2 * t;
    if P1 != None:
        tg2 = TENSION * (P3 - P1);
    else:
        tg2 = P3 - P2;
    if P4 != None:
        tg3 = TENSION * (P4 - P2);
    else:
        tg3 = P3 - P2;
    return (2 * t3 - 3 * t2 + 1) * P2 + \
        (t3 - 2 * t2 + t) * tg2 + \
        (-2 * t3 + 3 * t2) * P3 + \
        (t3 - t2) * tg3;

init ()
dpy = display.set_mode ((800, 800))

WHITE = (255, 255, 255)
GREEN = (0, 255, 0)
RED = (255, 0, 0)

# Control points
points = ((10, 10), (100, 200), (200, 300),
          (300, 500), (400, 400), (500, 500),
          (600, 200), (700, 100), (790, 790), (790, 790))

# Display a single-interpolated-coordinate spline
pi = 0;
p2 = (None, None);
p3 = points [0];
for x in range(points [0][0], points [len (points) - 1][0]):
    if (x >= p3 [0]) and (pi < len (points) - 1):
        p1 = p2;
        p2 = points [pi];
        p3 = points [pi + 1];
        if pi < len (points) - 2:
            p4 = points [pi + 2];
        else:
            p4 = (None, None);
        pi = pi + 1;
    t = float (x - p2 [0]) / (p3 [0] - p2 [0]);
    p = spline (p1 [1], p2 [1], p3 [1], p4 [1], t);
    draw.line (dpy, WHITE, (x, p), (x, p));

# Display a two-interpolated-coordinates spline
p2 = points [0];
p3 = points [0];
p4 = points [0];
for p in points:
    p1 = p2;
    p2 = p3;
    p3 = p4;
    p4 = p;
    t = 0.0;
    while t < 1.0:
        px = spline (p1 [0], p2 [0], p3 [0], p4 [0], t);
        py = spline (p1 [1], p2 [1], p3 [1], p4 [1], t);
        draw.line (dpy, GREEN, (px, py), (px, py));
        t = t + 0.01;

# Mark control points
for p in points:
    draw.line (dpy, RED, (p [0]-2, p [1]-2), (p [0]+2, p [1]+2));
    draw.line (dpy, RED, (p [0]-2, p [1]+2), (p [0]+2, p [1]-2));

# Display the stuff
display.flip ()

# Wait for ESC or close window
while True:
    for e in event.get():
        if e.type == QUIT or (e.type == KEYDOWN and e.key == K_ESCAPE):
            exit ()
    sleep (0.1)