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10# xyj200909


几张图,先增加一点感性认识:
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太撼人了,是真的还是虚幻的,亦真亦幻,不能不让人感叹数学和电脑科技的魅力
三元数组Mandelbrot球
mqiu.jpg
这些图应该是经过加工的吧,仅一个数学软件不易搞出这种效果。
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网上搜的,再发两个。http://www.subblue.com/projects/mandelbulb
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不好说,我们搞不出,也许有人能高出。
立体分形,要是靠立体切片扫描的话,几何画板是无法整出上面的效果的,扫描点不够,要是还用原来的扫描框扫立体图,就要考虑边界问题,想起了等势线作边界,也许可以,还有立体在平面上的投影。不过速度很难提。
大家翻译一下
How it works
The fractal calculation follows a similar process as a normal Mandelbrot set using the same formula,
w' = wn + c, but instead of using standard complex numbers w and c are hyper-complex 'triplex' numbers with three components corresponding to the Cartesian x, y, and z co-ordinates.

The triplex number w is raised to a power n using the following terms:

w = {x, y, z}n = rn { sin(θn) cos(φn), sin(θn) sin(φn), cos(θn) }

where:
r = sqrt( x2 + y2 + z2 )
θ = atan2( sqrt( x2 + y2 ), z )
φ = atan2( y, x )

The fractal is ray traced using basically the same process as the 4D Quarternion Julia set fractal; for each pixel a ray is stepped into the scene by a small amount. The x, y and z co-ordinates of the ray at this point provide the input triplex number for the fractal equation, which is then iterated until the magnitude of the triplex number exceeds a bailout value (usually 4.0), or the maximum iteration count is reached.

At the end of the iteration loop a distance estimation function is used to calculate the closest point in any direction to the fractal surface. It is defined as:

distance estimation = 0.5 * |w| * log(|w|) / |δw|

where |w| is the magnitude of the triplex number w and δw is the derivative.

The distance estimation value is crucial to the ray tracing process. It tells us the maximum step distance the ray can move before we need to recalculate the fractal at the new location, which is far more efficient than a fixed step ray marching approach.

When the distance estimation value drops below a defined threshold, epsilon, we are within intersection distance of the approximate fractal surface. If this happens we calculate the vector normal based on the fractal surface gradient, which defines the shading of that point.

http://www.subblue.com/blog/2009/12/13/mandelbulb
这样的分形确实很吸引人,我用软件作了一些效果图,可这里的上传受限,只好把图片发在这里了:http://cgpad.com/work/show/3963
19# xuefeiyang


非常吸引人,什么软件,能从中学点什么不。
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