Bezier curves
-
Upload
nikolay-yaremko -
Category
Documents
-
view
376 -
download
3
description
Transcript of Bezier curves
![Page 1: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/1.jpg)
Что мы знаем о кривых Бернштейна-Безье?
Что мы знаем о лисе?Ничего, и то не все.Б. Заходер.
![Page 2: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/2.jpg)
![Page 3: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/3.jpg)
![Page 4: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/4.jpg)
![Page 5: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/5.jpg)
Что мы знаем о кривых Бернштейна-Безье?
![Page 6: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/6.jpg)
![Page 7: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/7.jpg)
Полином Бернштейна, 1912 г.
![Page 8: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/8.jpg)
![Page 9: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/9.jpg)
Pierre EtienneBezier
![Page 10: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/10.jpg)
Pierre EtienneBezier
![Page 11: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/11.jpg)
![Page 12: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/12.jpg)
![Page 13: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/13.jpg)
![Page 14: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/14.jpg)
![Page 15: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/15.jpg)
![Page 16: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/16.jpg)
![Page 17: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/17.jpg)
![Page 18: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/18.jpg)
![Page 19: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/19.jpg)
Pierre EtienneBezier
![Page 20: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/20.jpg)
![Page 21: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/21.jpg)
![Page 22: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/22.jpg)
P(t)=(1-t)3P0 + 3t(1-t)2P1 + 3t2(1-t)P2 + t3P3
![Page 23: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/23.jpg)
![Page 24: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/24.jpg)
Pierre Bezier
1962
Renault
![Page 25: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/25.jpg)
Pierre Bezier
1962
RenaultPaul de Casteljau
1959
Citroën
![Page 26: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/26.jpg)
Pierre Bezier
1962
RenaultPaul de Casteljau
1959
Citroën
![Page 27: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/27.jpg)
Pierre Bezier
1962
RenaultPaul de Casteljau
1959
CitroënCarl de Boor
![Page 28: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/28.jpg)
![Page 29: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/29.jpg)
![Page 30: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/30.jpg)
![Page 31: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/31.jpg)
![Page 32: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/32.jpg)
![Page 33: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/33.jpg)
![Page 34: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/34.jpg)
![Page 35: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/35.jpg)
Что такого особенного в кривых Безье?
![Page 36: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/36.jpg)
Наглядно определяются контрольными точками
![Page 37: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/37.jpg)
Полностью лежат внутри фигуры из точек
![Page 38: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/38.jpg)
Инвариантны к повороту и изменению пропорций
![Page 39: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/39.jpg)
Инвариантны к повороту и изменению пропорций
![Page 40: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/40.jpg)
Легко переносятся в объём
![Page 41: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/41.jpg)
![Page 42: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/42.jpg)
Что изменилось сегодня?
![Page 43: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/43.jpg)
Процесс создания фирменного стиля Крымской федерации национальной борьбы куреш
Дизайн — это воплощение идеи
![Page 44: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/44.jpg)
Одна точка влияет на всю кривую
![Page 45: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/45.jpg)
Одна точка влияет на всю кривую
![Page 46: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/46.jpg)
Одна точка влияет на всю кривую
![Page 47: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/47.jpg)
Одна точка влияет на всю кривую
![Page 48: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/48.jpg)
Одна точка влияет на всю кривую
![Page 49: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/49.jpg)
Одна точка влияет на всю кривую
![Page 50: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/50.jpg)
Одна точка влияет на всю кривую
![Page 51: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/51.jpg)
Невозможно построить параллельные кривые
![Page 52: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/52.jpg)
Нельзя описать круг или эллипс,только приближения
![Page 53: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/53.jpg)
![Page 54: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/54.jpg)
Как человек воспринимает форму?
![Page 55: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/55.jpg)
![Page 56: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/56.jpg)
![Page 57: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/57.jpg)
![Page 58: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/58.jpg)
![Page 59: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/59.jpg)
![Page 60: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/60.jpg)
![Page 61: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/61.jpg)
![Page 62: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/62.jpg)
![Page 63: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/63.jpg)
![Page 64: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/64.jpg)
Мы воспринимаем мир как набор кругов
![Page 65: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/65.jpg)
А. Плахов, plakhov.livejournal.com
![Page 66: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/66.jpg)
А. Плахов, plakhov.livejournal.com
![Page 67: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/67.jpg)
А. Плахов, plakhov.livejournal.com
![Page 68: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/68.jpg)
А. Плахов, plakhov.livejournal.com
![Page 69: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/69.jpg)
А. Плахов, plakhov.livejournal.com
![Page 70: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/70.jpg)
А. Плахов, plakhov.livejournal.com
![Page 71: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/71.jpg)
А. Плахов, plakhov.livejournal.com
![Page 72: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/72.jpg)
А. Плахов, plakhov.livejournal.com
![Page 73: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/73.jpg)
![Page 74: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/74.jpg)
![Page 75: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/75.jpg)
![Page 76: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/76.jpg)
![Page 77: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/77.jpg)
Задача дизайнера — объяснить доступно.
![Page 78: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/78.jpg)
Мы должны работать с теми примитивами, что существуютв глазу пользователя, а не в инструменте для расчётов.
![Page 79: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/79.jpg)
![Page 80: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/80.jpg)
![Page 81: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/81.jpg)
![Page 82: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/82.jpg)
![Page 83: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/83.jpg)
![Page 84: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/84.jpg)
![Page 85: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/85.jpg)
![Page 86: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/86.jpg)
![Page 87: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/87.jpg)
![Page 88: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/88.jpg)
![Page 89: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/89.jpg)
![Page 90: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/90.jpg)
![Page 91: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/91.jpg)
![Page 92: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/92.jpg)
![Page 93: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/93.jpg)
![Page 94: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/94.jpg)
Дизайн — это намеренная ошибка.
![Page 95: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/95.jpg)
![Page 96: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/96.jpg)
![Page 97: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/97.jpg)
![Page 98: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/98.jpg)
![Page 99: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/99.jpg)
![Page 100: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/100.jpg)
Чем руководствоваться, выбирая форму юзерпика?
![Page 101: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/101.jpg)
![Page 102: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/102.jpg)
![Page 103: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/103.jpg)
![Page 104: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/104.jpg)
![Page 105: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/105.jpg)
![Page 106: Bezier curves](https://reader031.fdocument.pub/reader031/viewer/2022012916/548b3fd7b47959af428b46d6/html5/thumbnails/106.jpg)
Спасибо.