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以往我们在计算机中绘制曲线通常都使用鼠标来完成,但是鼠标并不是十分好控制,但是贝塞尔曲线的出现却使得利用鼠标描绘精确的线段成为可能。
贝塞尔曲线来自于数学领域,是应用于二维图形应用程序的数学曲线,同时它也是矢量线条的代表,其特点是用一组点和辅助线来表现一条线条的曲度、方向、位置等信息。
要画出完整、漂亮的贝塞尔曲线,熟悉并掌握贝塞尔工具可是关键。使用贝塞尔工具说容易也真太容易,初次接触者只需胡乱点击,就可以成为直线、折线,而按着鼠标移动,就成了曲线!但是如果要掌握贝塞尔工具使用的精髓却是非常的难,它是所有工具中最难的,如果我们没有经过艰苦的练习,肯定掌握不了!
下面我们就从贝塞尔的基本操作入手,来熟悉并掌握它。
第一,直线的画法:选择好贝塞尔工具,然后在工作区的任意一个位置点击一下鼠标左键,这样就确定了第一个节点位置,接着松开鼠标左键后,在工作区的另一个位置上再点击一下鼠标左键,这样就确定了第二个节点,此时两个节点之间就会出现一条直线,按空格键或者点击其他工具即可结束直线的绘制,如图1所示。另外在选中状态下的线段路径起点处的节点要比结束端的节点大。
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(图1 )
第二,折线的画法:折线的画法也是非常简单的,我们只需要在直线的基础上,再在其他位置上点击鼠标左键,这样就绘制出来了折线,如图2所示。
![](https://www.soolun.com/img/pic.php?url=data:image/png;base64,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(图2)
第三,曲线的画法:绘制曲线是贝塞尔工具的最拿手的操作,也是体现它精确绘制圆滑曲线的精华之处,说到使用贝塞尔工具较难,一般也都指的是利用贝塞尔工具绘制曲线。下面我们就以绘制一条曲线为例,来熟悉一下贝塞尔工具绘制曲线的使用方法:
第一步:一条曲线一般由起始点、终点以及中间的一些节点组成。选中贝塞尔工具后,首先在工作区中任意位置上单击一下鼠标左键,以确定出来曲线线段的起始点。
第二步:接着在工作区的其他位置上再次单击鼠标左键创建一个节点,但这时不要松开鼠标,继续按住鼠标左键并拖动一段距离,这时我们可以看到此时该节点两边出现两个控制点,连接两个控制点的是一条蓝色的控制虚线,同时线段会随着控制线的改变发生弯曲。
第三步:按照上面的方法,再绘制出第三个节点,同样也是创建出节点后再按住鼠标左键不放,拖动鼠标调节控制点连线的长度和角度,这样调整完成后,释放鼠标即可完成曲线线段的绘制,如图3所示。
![](https://www.soolun.com/img/pic.php?url=data:image/png;base64,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)
(图3)
强调一点:我们对于直线的画法通常都采取“两点确定一条直线”方法,而实际上直线也是曲线的一种,如果我们多绘制出来几个节点,而设置贝赛尔曲线的曲率为零,这也是直线,所以说曲线形状是由节点延伸出来的隐藏的切线决定的,我们从图3中就可以体会出来,两个节点处的控制线长短不同,方向不同,所产生的曲线弯曲程度、角度也不同。
上面我们讲述了如何使用贝塞尔工具来绘制贝塞尔曲线的方法,而对于使用不同的工具时,虽然它们的贝塞尔工具名称不相同,但都可以用来画出各种路径的图形。比如我们要绘制一条波浪曲线,我们可以使用Photoshop中的“钢笔工具”,Fireworks中的“钢笔工具”以及CorelDraw中的“贝塞尔工具”等,利用这些工具绘制出来的曲线效果如图4所示。
![](https://www.soolun.com/img/pic.php?url=data:image/png;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwgHBgoICAgLCgoLDhgQDg0NDh0VFhEYIx8lJCIfIiEmKzcvJik0KSEiMEExNDk7Pj4+JS5ESUM8SDc9Pjv/2wBDAQoLCw4NDhwQEBw7KCIoOzs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozs7Ozv/wAARCABcAicDASIAAhEBAxEB/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/8QAHwEAAwEBAQEBAQEBAQAAAAAAAAECAwQFBgcICQoL/8QAtREAAgECBAQDBAcFBAQAAQJ3AAECAxEEBSExBhJBUQdhcRMiMoEIFEKRobHBCSMzUvAVYnLRChYkNOEl8RcYGRomJygpKjU2Nzg5OkNERUZHSElKU1RVVldYWVpjZGVmZ2hpanN0dXZ3eHl6goOEhYaHiImKkpOUlZaXmJmaoqOkpaanqKmqsrO0tba3uLm6wsPExcbHyMnK0tPU1dbX2Nna4uPk5ebn6Onq8vP09fb3+Pn6/9oADAMBAAIRAxEAPwD2aiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAooooAKKKKACiiigAqCFWgPlvI8gZiVZzk8nOPw7e1T010DrtP/AOqgB1FRxufuP98fqPWpKACiiigAooooAKKKKACiiigAooooAKKKKACiiigBkjiKNpCCQoyQoyfypykMoYHIPSlqFP3Mnl/wN932PpTAmooopAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFFISAMngVF9oDcRKZPccD86AJqKhzcntEv1JNH+kj/AJ5N+Y/xoAmoqHz9n+uQx+/UfnUoIIyOhoAWiiigAooooAKKKKACiio5Zlh2ZVmLsFAUZP1+lAElFFFABRRUU88dvHvkJA6AAEkn0AHU0AS0hIAyTiqmLq6yS7WsZ6BQC59zngUo021K4lQz85/fMX5/HinYV30LQIPQ0tVBplmqsI4Fi3dTFlD+YpPKu7bmKU3CD/lnL978G/xo0C7LlFQwXMc4O3Ksv3kYYZfqKmpDCiiigAooooAKKKiuZHigZ40DuMYUnAJz60JXE3ZXJaKKKBhRRRQAUlI7rGu5jxUYjabmbhe0f+PrQAfaEJxGrSf7o4/PpR5sv/Pu2P8AeH+NSgADAGBS0AV2kRyOscg+6HGM+3vUyOJFyOOxHoaGVXXayhgexqu6vbN5i5eP+IdSB/XFAFqikVg6hlOQeQRS0AFFFFABRRRQAUVUOowDURY/P5pTfny224zjrjFW6ACiiigAooooAKKKhmuo4WCYLyN92NBlj/gPc0ATUyRBIhU/gfSq/wDp8vOYYB6YLn+gpfLvkGRPDL7NGV/UH+lO3mK5NE5YFX++vB/xqSqTXJEil42imHG0nIkHoD3P61cVg6hgcgjIoaAWiiikMKKKKACiiigAooooAKKKKACopZ0iKqTl3+6vdqlppVSwYqCR0OOlAEYiMnzTHPog6D/GpelLRQAUUUUAJURiMZ3Q8eqdj9PSpqKAI4Z451JRs7Thh6H0qSq80DbvOgIWUdj0f2P+NOhuEl+U5Rx1VutAE1FFFABRRTXkSMZdgB70AKSFBLEAAZJNVrOX7WpuijoGyqLIuCAO+Pf+WKbKHupkheNliI3HI4IHYn+lW6AFooooAinmWCPeQTk4AHUk9BUcFs3mm4nIaUjAA6IPQf41YpaBW1CiiigYUUUUAV7q2Myh4pDFMv3XH8iO4p0E4lBVhslXh0PY/wCFTVWuoHYie3wJ487cnAcf3T7fypol6aos0VXtbtLpDgFJF4kjb7yH0NWKRSdwooooAKguHXzIoiwDO2QCeTjmp6oxn7TqjSlAY7ddsbdyx+8R+WPzqkTLsXqKKKkoKKKKAK8cc5uZHnaNkB/chQcgd8+9WKKKACiiigAooooApEzWt4qhEFkynLZ5R8+n90/zq7SMqupVgCpGCD3qokjWTeVMS0P8Eh/hHof8aALlFICCMg5BpaACiiqsp+1loFP7rpKwPX/ZH9aAKttDPfpPLcz7VeVhA1vlG8sHjJ/M8cHNaSKEQKM4Hqc0kMUcEKQxLtjjUKq+gHSn0AFFFFABRRSNnaduM44zQBXuJ38wW9vgysMknog9T/Qd6kgt0t1O3LM3LO3LMfc021gMER3ndK53SP8A3j/h2qem+wBRRRSAZJEk0ZSRQynsaqwmSzuPs8pLRSHMUh9f7p9/51dqOaJZ4jG44P6e9NPoKxJRUNu8hUxzEean3sdCOxqak9BhRRRQAVWa+hS+S0c7XdSVJ6EjqPrT7mUxqqJjzJDhB/M/QUqQRptO0My5+YjnnrTAlooopAFFFFABRRRQAUUUUAFFFFABRRRQAVDPAH+YKC3cHv8A/X96mooArorlcxTHA4KyDOPb1p+bj+7F/wB9H/CiSNg3mR/e7jswp0cgkXIz6EHqDQAzbcN1dE/3Rn+dOSFUO45Zv7zcmpKKACiiigAooooAKKKKACiiigAooooAKKKKAKlzanzPtMJ2SgYJAzke470LfBMC5Xys9JCfkb6Ht+NW6gYCInIzE/3gRwP/AK1Pchq2qJgQQCDkHuKRmVFLOwVRySTgCq5061IbYjRbjkmJynP4GhdOtVKsyNIy5w0rlyPzNGhWohma7Jjg3LH/ABTYx+C+p96ktrc2+9QwKEjYoXG0AAY96mpaLit1YUUUUigooooAKKKKACiiigAooooAKZIgkXB4PY+lPooAppAyki3k8lh95CMoffHb8Kk33g4MMLe4kI/pUkiE/Ov31/X2pyOHXcP17UAQeTPNxPKFX+5FkZ+p6/lip0RUUIihVHAA7U6igAooooAKKKKACiiigAooooAKKKKACiiigCC4jcgSxf6xOg/vDuKfDKs0YdfxB7VJVV4zFNvQ7d5644B9/Y099BFqkqLzpF4eFifVORSfvJuCpjTuD1P+FFhjYIg1xJclmYN8qZ7D2/GrNIAAABwBS0N3AKKKKQBRRRQAUUUUAFFFFABRSUtABRSUtABRRRQAVH5Kef53zbtu3rwfwp9LQAUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAUUUUAFIQCMEZFLRQBCv7lhGfuH7p9PapqjmhSeJopASjDBAOP1FPAAAA6CmJXQtFFFIYUUUUAFFFFABRRRQAUUUUAFFFFABRRRQAVXuJPsqtPsd143Kilie2QBViigAooooAKKKKACiiigAooooAKKKKACiikoAWiiigAprqHUqwyDTqKAIonbmNzll7+o9alqKZGOHT76dPf2p6OJEDDoaAHUUUUAFFFFABRRRQAUUUUAFFFFACVlR6LNEXEeqXKpJncuc889Cc469vQVrUUAZcmlXbzLINXuF2kkAKuOc/4/oKgbw607rLdajcSyqjoDnC4Y8ZX2H51t0UAc2vhEqFCanMvlqVQBcBc554PXnr9Khj8EvHEqf2zdErnaecDr2z7muqooA5tfCLqy7dWuQgGCozzkEE5z15zWpo2lf2PZm2+1S3AyCHlOSAABj9K0KKACiiigAooooAKKKKACiiigAqvdw3Eyx/Z7jySrbjxndweD7Zx+VWKKAM9rfVcnbfwj5eAYO/51E2n6nIV36qQqvuHlxgEjng/mPyrVooA586PrYUhdZPAYLnPU9z9PSmR6Jr42+ZrzNxhgFx+Xv710dFAGAmka75sbSa2SqSbioT74x0Nb9FFABRRRQAUUUUAFFFFABRRRQAUUUUARzpJJEVik8tsj5sZ71RktdWdQBqESn1WH/wCvWlRQBmyWeqSkZ1NY1VlIEcIBIxyCST1qm2k675ZVNbw2CFPl+vc1vUUAc+uk6+MFtdycc/ugOcf41ZstP1iG7jlutWE8Sgh4hGAG64OfxH5Vr0UAFFFFABRRRQAUUUUAFFFFABRRRQBlf2RcrE0cWq3CKxJJ+8Tn3PT8Kgl8NeY28ajc+Z5nmbnbdzgDgdvX/wDVW5RQBzT+EJHkRhrV4qqpUqGPzZOSSc05PCsyBdus3YKsDnJ5x0HX/Oa6OigDP0fSzpNu8P2ua5DNuDTHJHtmtCiigAooooAKYkSxs7LnLnJ570+igAooooAKKKKACiiigD//2Q==)
(图4)
我们从图4中可以看出,无论使用哪种设计软件来创建这条波浪曲线,它们都是向曲线的隆起方向拖移第一个控制点,并向相反方向拖移第二个控制点,而同时向一个方向拖移两个控制点将创建波浪曲线。其操作特点都是通过用鼠标在面板上放置各个锚点,根据锚点的路径和描绘的先后顺序,产生直线或者是曲线的效果。那么根据前面所学到的知识点,大家可以利用任何一种软件中的贝塞尔工具来绘制如图5所示的“S”字母,要注意一点的是,两条曲线要平行,这样才能达到预期的效果,相信大家在这个实例制作过程中能够更好地将贝塞尔工具的用法以及技巧熟悉并掌握。
![](https://www.soolun.com/img/pic.php?url=data:image/png;base64,/9j/4AAQSkZJRgABAQEAYABgAAD/2wBDAAoHBwgHBgoICAgLCgoLDhgQDg0NDh0VFhEYIx8lJCIfIiEmKzcvJik0KSEiMEExNDk7Pj4+JS5ESUM8SDc9Pjv/wAALCACXAG8BAREA/8QAHwAAAQUBAQEBAQEAAAAAAAAAAAECAwQFBgcICQoL/8QAtRAAAgEDAwIEAwUFBAQAAAF9AQIDAAQRBRIhMUEGE1FhByJxFDKBkaEII0KxwRVS0fAkM2JyggkKFhcYGRolJicoKSo0NTY3ODk6Q0RFRkdISUpTVFVWV1hZWmNkZWZnaGlqc3R1dnd4eXqDhIWGh4iJipKTlJWWl5iZmqKjpKWmp6ipqrKztLW2t7i5usLDxMXGx8jJytLT1NXW19jZ2uHi4+Tl5ufo6erx8vP09fb3+Pn6/9oACAEBAAA/APZqKKTvTXdIkLyOFVeSzHAFclqfxK0Oyn+zWfm6ncdPLtV3Yqmvi7xfffNY+FniQ/dNzkGnnWPiCFz/AGJYk+m9qYfGPiyyIN94UllQdTbZNXNN+JehXk/2e8MumT9Nl0u3mutjkSWNZI3DowyCpyDThS0UUUmay/EHiGw8N6c17fSYHREHLOfQCuNh0fxD4/kF5rcsmmaQTmOyjOHkH+16V2ek+HNI0S3WHT7GKIL/ABbQW/PrWnRmjNZmq+HtI1uAw39jFKp77QG/OuKn0/WvhxKbzTpZNR0InMts5y8A9V9a7zStUtNY06G/spBJDMuVI7e1XM0tFITVe/vYNOsZry5cLDChdmPoK4Pwxps/jTWD4r1qMm0RiNPtm+6B/fIr0PGOOAKqanqtjo1m13qFykES92OM+w9a49viTPfyFdA0G6vk7SSKUU/Q05vFnjNF3v4PXYOuLjJqbTfiVp0lytnrFpPpVw5wPPTCE/71dkrrIgdGDKwyCDwRSSRpLG0cihkcbWU9CK88sS/gDxr/AGazN/YurNmDPSGX+79K9FzxnqPWlpaQ1wfxInlv59L8MW5O7UJg8oXr5ankV21paxWVpFa26hYoUCqo7AUy/vYdOsJr24YLHChZifauC0DRp/Ht9/wkviFSbEN/oNkfu7QfvMO9ehwQxW8axQxrHGowFUYAqSs/WNE07XbRrXUbVJkYYBYcr7g9q4zw/e3ngvxKvhbU52n0+550+4c8j/YJr0L8K5rx9of9t+FrhIgftNv++gYdVYc1Y8Gaz/bvhazvGI8zZskHow4NbtLRXBxj7b8YHZvmFja4APbcK7vv0ri/ilNKfC62UXBu50Rj7ZGa6vT7WKx0+3tYV2xxRhQKsilpDXH/ABM00XnhZryMYubB1micdVwea6DQb86poNlfHrPCrGrzrvjZT/ECK4f4bqbK81/STwLS8+UegPNd0KWkrhtLbb8WtWVhjfbptPrxXc1xfxShkHhhb2Pn7JOkjD2yM11lhdRXunwXMLbo5Ywyn8KsClpO9Z+vWL6loV5ZRcPNCyr9SK4rR1+IOjaRa6dFp9i8dtGEVmJyQPWrv9ofEXtpun/mal8FaLrlnrOrarrKRRPfuG2R9BgV2YpaQ15/4lf/AIR/4jaRrJz9nvFNvMewY8CvQM/lVbULCDU7CayuUDRTIVIPvXBeHdbm8DXv/CMeIWZbQMfsN4w+QrnhSa9EjdJEEkbB0YZBByDTqKKKMUYopaQ1ieLPD0fiXQZrBjsl+/C/dXHQ1leBfE0l7A+hasDDq9h8jo/HmKOjD1rsPTiqOraPp+uWT2eo2yTxNxgjkfQ9q4pvDXinwfIZfDd5/aFgDuNlcNyo9Aav6V8S9NnlW01mCbSLvoVuFwmfY12EE8N1Cs0Eqyxt0ZDkGpKWiiiiikxXL+LfBq64yajp85stXt+Ybhe/+y3qKztF8fSWt2ujeLLc6ffj5VmP+ql9we1dsjpIivGyujDIZTkGnVR1TQ9M1mExahZRTgjGWUEj6GuPuPh9qGjSm68JaxLalefs07b0PsPSn2XxButKul0/xfpz2Ep4W5Qbon/HtXcQXMF1Cs9vKksT/ddDkGpKWiiiikNZ+saHp2vWhtdRtUnjIwCw5X3BrjW8LeKPCbmbwxqJvbMf8uNydxA9Aataf8TbJZvsniCyn0m6BxiRSUJ+tdla3ltfQia1uI5kI4ZGBFTVWv8ATrPVLVrW+t0uIWHKuMiuDufDet+B521DwvK95p+czadIc4HfbXWeGvFGn+J7H7RaPtlT5ZoH4eNvQitqiiiiiikqpf6XYapAYb+0juIz2dc1x158O7nTJTeeEtUl0+XOfszsTE3til03x/c6deJpni+xbT7hjhLkD91J/hXcRypLGJI3V0YZVlOQad04rhvFfhu50y8PirwyPLvYebm3XhbhO/HrXSeHNftfEujxahanbu4eM9UbuDWtS0UmaKKKKMVS1TSLHWbN7PULdJ4nGCGHI+hrhP8AiZ/DK9TfJLfeGpW2knl7Un+leh29xDd28dxbyCSKRdyMp4IqQgEYPIPb1rzy0T/hDfiQ1kh26ZrY3og6JL6V6IKWqOs350rR7u/CbzbxF9p74rjbHxj4y1KyjvLXw3bNDKMoTKckVY/4SLxz/wBC1bf9/TVzwn4q1DXNRvdP1LT0s57QAkIxOa6yiikNV72zg1Gzms7mMSRTKVZSM8GuK+H00+katqnhK5cstm3m2xY/8syeBXe9BXEfE+HZp2m6jGMSWd4jhu4FdnbSedaxSn+NFb8xUtY3i5S/hLU1HU27VX8CSCTwdp5B6RgV0FcN4ccxfE3Xrd+GaBHGe/Nd1RRSUYrhSB/wuRtnDfYF34+veu6rj/icwXwtg9WmUAevNdRp3GmWoP8AzxT+QqzVXUrX7bptxa/89Yyv5iuU+Ft2JPDD2Tn99Z3Ekbg/Xiu0rz/xM58N/EPTdec7bS+X7NO3ZcdCa9ADBlDAggjIPrRS0U2SRIo2kdgqICzE9gK4HwKX1vxVrXiU8wO32a3Y9wp6iu/H5VwnxJl+1XOh6PHzJc3qsR/siu5jQRxIg6KoAp9JXndtJ/wh3xKmgm/d6drY3RMeiyDt+Neh1na/olp4g0ibTrxfkkHDDqp7EVxuk+J73wZcJoPisObdTttNQAyrL2De9d9bXVtdxCS2njmRhkMjA1NUU9zBaoZLieOJQMkuwFef654kufGly3hzwvuNu5xeX4GFVe4Fdvouk2uh6TBp1mgWKFdufU+pq6SFBJ4A5J9K8+0Zj4t+I91q4G/T9JUwQP2Z/UV6FS0lYXi7wzF4m0ZrXd5VzGfMt5R1Rx0rM8GeK5bvdoWtgW+sWnysrcCZR0Yetdfj26dKrX+nWeqWrW19bJcRN1VxmuQf4ZRWkry6DrV7phY/6uN8pR/wiPiwrsPiyfH94daF+GUN1Ismt63f6lg5Mcj4Q112naXY6RaC20+1jt4h0VBVoAAVw3jDxLcahdf8Ir4cbzL+4+W4mXkW6dzn1rpvDmg23hzRoNOthkIPnc9XbuTWoKWkornPFXg618RxpcRyNaajBzBdR8Mp9/UVgW/jLXfCriy8Xae80S8LqFuu5W92rrdM8TaLrKqbDUYJsjO0NgitQEdmB/GlprOq8llA7kmsTVvGnh/RUb7XqMXmL0iQ5Y/QCuYl13xP42Y2ug2kmlac3D3s4w7DvtFdT4Z8Kaf4YsvKtgZJ5OZbh+XkPqTW3S0UlFFMlhinjMc0aSIequoIrmdQ+G/hrUJWm+xtbyn+KByn8qzh8NZrfiy8R30CjoCd2PzNOPgLWSMf8Jfef9+x/jSf8KxjuCP7Q1y+uV7jeVz+RrX0vwF4c0mQSwaeskg/jmPmH9a6FUVFCooVR0AGAKWjFFf/2Q==)
(图5)
综上所述,使用“贝塞尔工具”不但在绘制一些图形,甚至在绘制卡通图像、描绘建筑物方面都得心应手,而大家只有通过多次练习并绘制出来一些图形作品,才能够熟练掌握“贝塞尔工具”使用技巧和方法,从而使自己的艺术作品锦上添花。
贝塞尔曲线来自于数学领域,是应用于二维图形应用程序的数学曲线,同时它也是矢量线条的代表,其特点是用一组点和辅助线来表现一条线条的曲度、方向、位置等信息。
要画出完整、漂亮的贝塞尔曲线,熟悉并掌握贝塞尔工具可是关键。使用贝塞尔工具说容易也真太容易,初次接触者只需胡乱点击,就可以成为直线、折线,而按着鼠标移动,就成了曲线!但是如果要掌握贝塞尔工具使用的精髓却是非常的难,它是所有工具中最难的,如果我们没有经过艰苦的练习,肯定掌握不了!
下面我们就从贝塞尔的基本操作入手,来熟悉并掌握它。
第一,直线的画法:选择好贝塞尔工具,然后在工作区的任意一个位置点击一下鼠标左键,这样就确定了第一个节点位置,接着松开鼠标左键后,在工作区的另一个位置上再点击一下鼠标左键,这样就确定了第二个节点,此时两个节点之间就会出现一条直线,按空格键或者点击其他工具即可结束直线的绘制,如图1所示。另外在选中状态下的线段路径起点处的节点要比结束端的节点大。
(图1 )
第二,折线的画法:折线的画法也是非常简单的,我们只需要在直线的基础上,再在其他位置上点击鼠标左键,这样就绘制出来了折线,如图2所示。
(图2)
第三,曲线的画法:绘制曲线是贝塞尔工具的最拿手的操作,也是体现它精确绘制圆滑曲线的精华之处,说到使用贝塞尔工具较难,一般也都指的是利用贝塞尔工具绘制曲线。下面我们就以绘制一条曲线为例,来熟悉一下贝塞尔工具绘制曲线的使用方法:
第一步:一条曲线一般由起始点、终点以及中间的一些节点组成。选中贝塞尔工具后,首先在工作区中任意位置上单击一下鼠标左键,以确定出来曲线线段的起始点。
第二步:接着在工作区的其他位置上再次单击鼠标左键创建一个节点,但这时不要松开鼠标,继续按住鼠标左键并拖动一段距离,这时我们可以看到此时该节点两边出现两个控制点,连接两个控制点的是一条蓝色的控制虚线,同时线段会随着控制线的改变发生弯曲。
第三步:按照上面的方法,再绘制出第三个节点,同样也是创建出节点后再按住鼠标左键不放,拖动鼠标调节控制点连线的长度和角度,这样调整完成后,释放鼠标即可完成曲线线段的绘制,如图3所示。
(图3)
强调一点:我们对于直线的画法通常都采取“两点确定一条直线”方法,而实际上直线也是曲线的一种,如果我们多绘制出来几个节点,而设置贝赛尔曲线的曲率为零,这也是直线,所以说曲线形状是由节点延伸出来的隐藏的切线决定的,我们从图3中就可以体会出来,两个节点处的控制线长短不同,方向不同,所产生的曲线弯曲程度、角度也不同。
上面我们讲述了如何使用贝塞尔工具来绘制贝塞尔曲线的方法,而对于使用不同的工具时,虽然它们的贝塞尔工具名称不相同,但都可以用来画出各种路径的图形。比如我们要绘制一条波浪曲线,我们可以使用Photoshop中的“钢笔工具”,Fireworks中的“钢笔工具”以及CorelDraw中的“贝塞尔工具”等,利用这些工具绘制出来的曲线效果如图4所示。
(图4)
我们从图4中可以看出,无论使用哪种设计软件来创建这条波浪曲线,它们都是向曲线的隆起方向拖移第一个控制点,并向相反方向拖移第二个控制点,而同时向一个方向拖移两个控制点将创建波浪曲线。其操作特点都是通过用鼠标在面板上放置各个锚点,根据锚点的路径和描绘的先后顺序,产生直线或者是曲线的效果。那么根据前面所学到的知识点,大家可以利用任何一种软件中的贝塞尔工具来绘制如图5所示的“S”字母,要注意一点的是,两条曲线要平行,这样才能达到预期的效果,相信大家在这个实例制作过程中能够更好地将贝塞尔工具的用法以及技巧熟悉并掌握。
(图5)
综上所述,使用“贝塞尔工具”不但在绘制一些图形,甚至在绘制卡通图像、描绘建筑物方面都得心应手,而大家只有通过多次练习并绘制出来一些图形作品,才能够熟练掌握“贝塞尔工具”使用技巧和方法,从而使自己的艺术作品锦上添花。