派︰昔有『 Thue 』者,其言曰︰
阿克塞爾‧圖厄【挪威語 Axel Thue】一位數學家,以研究丟番圖用『有理數』逼近『實數』問題以及開拓『組合數學』之貢獻而聞名。他於一九一四發表了『詞之群論問題』Word problem for group 啟始了一個今天稱之為『字串改寫系統』SRS String Rewriting System 的先河,如從現今的研究和發現來看,它與圖靈機的『停機問題』密切相關。上個千禧年之時,John Colagioia 用『Semi-Thue System』寫了一個『奧秘的』 esoteric 程式語言 Thue ,作者宣稱︰
Thue represents one of the simplest possible ways to construe 『constraint-based』基於約束 programming. It is to the constraint-based 『paradigm』典範 what languages like『 OISC 』── 單指令集電腦 One instruction set computer ── are to the imperative paradigm; in other words, it’s a 『tar pit』焦油坑.
,果然概念廣大能通天!!『 SRS 』卻是個『奧秘語言』??
洛基的賭注 Loki’s Wager
洛基乃北歐神話中以『詐騙』著名之神。傳說他曾與矮人打賭卻輸了。當矮人們依約來『提頭』時,洛基說︰『沒問題』,但是必須依照『約定』,只能取走『他的頭』,而不能動著『他的脖子』。於是彼此開始『爭論』該如何的『切割』:有哪些部分雙方同意『是頭』;又有哪些部分認同『是脖子』。只是脖子的『結束點』和頭之『開始點』究竟『是哪裡』,互相一直無法『取得共識』。於是洛基終於保住著了他的頭。
── 摘自《M♪o 之學習筆記本《丑》控制︰【黑水北】當思恒念》
當『數理』失卻了『參考系』確定『概念』之意義;宛如憑空地述說著『群論』可以將一元多次方程式可解性的問題連繫起來,豈非囫圇吞棗乎?不知滋味之物要怎樣講耶??
且思『近』之『視角大』、『遠』之『視角小』是『歐式幾何』之『性質』嗎?
可以得到
然而『天很高,日很遠』,因此 ,故而很難『度量』的『精準』,一點點『角度』之『誤差』就產生了那個
失之豪釐,差以千里
的吧!!
─── 摘自《失之豪釐,差以千里!!《上》》
難到『有限高度』 之物,若位在『無窮遠』 處,竟然它的『視角』 能不趨近於『零』 嗎??
就像『眼見之實』
消失點
如當你沿著鐵路線去看兩條鐵軌,沿著公路線去看兩邊排列整齊的樹木時,兩條平行的鐵軌或兩排樹木連線交與很遠很遠的某一點,這點在透視投影中叫做消失點。
藝術家和工程師在紙上表現立體圖時,常用一種透視法,這種方法源於人們的視覺經驗:大小相同的物體,離你較近的看起來比離你較遠的大。凡是平行的直線都消失於無窮遠處的同一個點,消失於視平線上的點的直線都是水平直線。
之『現象文字』及『理論內容』的陳述
Vanishing point
In graphical perspective, a vanishing point is an abstract point on the image plane where 2D projections (or drawings) of a set of parallel lines in 3D space appear to converge.[clarification needed] When the set of parallel lines is perpendicular to a picture plane, the construction is known as one-point perspective, and their vanishing point corresponds to the oculus, or “eye point”, from which the image should be viewed for correct perspective geometry.[1] Traditional linear drawings use objects with one to three sets of parallels, defining one to three vanishing points.
A 2D construction of perspective viewing, showing the formation of a vanishing point
需要『想像』呦!
The vanishing point may also be referred to as the “direction point”, as lines having the same directional vector, say D, will have the same vanishing point or converge at the same vanishing points. Mathematically, let q ≡ (x, y, f) be a point lying on the image plane, where f is the focal length (of the camera associated with the image), and let vq ≡ (x/h, y/h, f/h) be the unit vector associated with q, where h = √x2 + y2 + f2. If we consider a straight line in space S with the unit vector ns ≡ (nx, ny, nz) and its vanishing point vs, the unit vector associated with vs is equal to ns, assuming both are assumed to point towards the image plane.[2]
When the image plane is parallel to two world-coordinate axes, lines parallel to the axis which is cut by this image plane will meet at infinity i.e. at the vanishing point. Lines parallel to the other two axes will not form vanishing points as they are parallel to the image plane. This is one-point perspective. Similarly, when the image plane intersects two world-coordinate axes, lines parallel to those planes will meet at infinity and form two vanishing points. This is called two-point perspective. In three-point perspective the image plane intersects the x, y, and z axes and therefore lines parallel to these axes intersect, resulting in three different vanishing points.
不知可否借假修真的哩◎