📚 Year 12 CIE Art & Design: Quick Reference Handbook of Formulas and Principles | Year 12 CIE 艺术与设计：公式定理速查手册
Mastering visual composition in CIE Art & Design requires more than intuition; it demands a working knowledge of the underlying 'formulas' and perceptual theorems that shape proportion, colour, depth, and form. This quick-reference handbook compiles the essential principles every Year 12 student needs, from the mathematics of beauty to the science of seeing.
在 CIE 艺术与设计课程中，掌握视觉构图不仅靠直觉，更需要理解塑造比例、色彩、深度与形态的底层"公式"与感知定理。这本速查手册整理了每位 Year 12 学生必备的核心原理，从美的数学到观看的科学，一应俱全。
1. Golden Ratio & Phi | 黄金比例与 φ 值
y dividing a line into two parts so that the whole length divided by the longer part equals the longer part divided by the shorter part. This proportion appears in the Parthenon, the human face, and countless compositions across art history.
将一条线段分为两段，使全长与较长段之比等于较长段与较短段之比，即得到黄金比例（φ ≈ 1.618）。这一比例出现在帕特农神庙、人类面部以及艺术史上无数构图之中。
φ = (1 + √5) / 2 ≈ 1.618
2. Rule of Thirds | 三分法则
The Rule of Thirds divides the canvas into nine equal parts using two equally spaced horizontal lines and two equally spaced vertical lines. Placing key elements along these lines or at their intersections creates balance and allows the eye to move naturally through the work.
三分法则用两条等距水平线和两条等距垂直线将画面分成九等份。将关键元素放置在这些线条上或交点处，能创造平衡，并引导视线在画面中自然流动。
3. Fibonacci Spiral Composition | 斐波那契螺旋构图
The Fibonacci spiral, built from a sequence where each number is the sum of the two preceding ones (1, 1, 2, 3, 5, 8, 13…), produces a logarithmic spiral that approximates the Golden Ratio. Many Renaissance painters used this spiral to guide the viewer’s eye toward the focal point, creating a dynamic yet harmonious flow.
斐波那契螺旋由数列（1, 1, 2, 3, 5, 8, 13… 后一项为前两项之和）衍生而来，形成近似黄金比例的对数螺旋。许多文艺复兴画家用此螺旋将观众视线引向焦点，营造出动感而和谐的走向。
4. One-Point Perspective | 一点透视
ch time the distance from the viewer is doubled, which can be expressed as a simple mathematical relationship: height’ = height × (distance to picture plane / distance from viewer).
在一点透视中，所有向后延伸的平行线汇聚于视平线上的一个消失点。物体距离观者每增加一倍，其表观尺寸减半，可用简单数学关系表达：高度’ = 高度 ×（画面距离 / 观者距离）。
Apparent size ∝ 1 / distance
5. Two-Point Perspective | 两点透视
Two-point perspective uses two vanishing points placed on the horizon. Vertical edges remain vertical while horizontal edges recede toward the left or right vanishing point. The station point and cone of vision determine the degree of distortion; an angle of 60° is standard for a natural look.
两点透视在视平线上使用两个消失点。垂直边保持垂直，水平边则分别向左、右消失点退缩。视点和视锥决定了变形程度；标准的自然视角通常采用 60° 视锥角。
6. Atmospheric Perspective | 空气透视
lighter in value, and shift toward blue-grey hues. The formula: contrast reduction ≈ 1 / ek·d, where d is distance and k is a coefficient affected by humidity and particulate density. This optical principle is vital for creating believable depth in landscapes.
空气透视描述远处物体如何失去对比度、明度变亮并向蓝灰色调偏移。公式：对比度衰减 ≈ 1 / ek·d，其中 d 为距离，k 为受湿度和微粒密度影响的系数。这一光学原理对在风景画中创造可信的空间深度至关重要。
7. Complementary Colour Contrast | 互补色对比公式
The afterimage rule states that staring at a colour fatigues specific cone cells, producing an afterimage in its complementary colour. This biological 'formula' is why juxtaposing complements (red–cyan, blue–yellow, green–magenta) generates the highest visual vibration and maximum contrast.
残像定则指出，盯着一种颜色会使相应视锥细胞疲劳，产生该颜色互补色的残像。这一生物"公式"解释了为何并置互补色（红–青、蓝–黄、绿–品红）会产生最强烈的视觉振动和最大对比度。
8. Simultaneous Contrast (Chevreul’s Law) | 同时对比（谢弗勒尔定律）
Chevreul’s Law: when two different colours are placed side by side, each appears to shift slightly toward the complement of the other. For a mid-grey patch on a red ground, the grey will appear tinged with green–cyan. This principle is essential for colour mixing and avoiding muddy neutrals.
谢弗勒尔定律：当两种不同颜色并置时，每一方在视觉上都会略微偏向另一方的补色方向。例如，在红色背景上的中灰斑块会呈现青绿色调。理解此原理对于色彩调和及避免脏中性色至关重要。
9. Colour Harmony Schemes | 色彩和谐搭配公式
Colour harmony can be expressed as geometric selections on the color wheel. The following table summarises the key schemes and their angular relationships.
色彩和谐可表达为色轮上的几何选择。下表总结了主要搭配方案及其角度关系。
| Scheme / 方案 | Angle / 角度 | Example / 示例 |
|---|---|---|
| Complementary / 互补 | 180° apart / 相隔180° | Red + Cyan / 红 + 青 |
| Split-Complementary / 分裂互补 | Base + two 150° offsets / 基色 + 两侧150° | Blue + Yellow-Orange + Red-Orange |
| Triadic / 三元组 | 3 colours 120° apart / 相隔120°的三色 | Red, Yellow, Blue |
| Tetradic / 四元组 | Two complementary pairs, 90° or 120° spacing / 两组互补对，间隔90°或120° | Red, Green, Blue, Orange |
10. Gestalt Principles of Visual Grouping | 格式塔视觉组织原则
Gestalt theory offers a set of perceptual 'theorems' that describe how the brain organises visual elements into unified wholes. The six classic principles—similarity, proximity, continuation, closure, figure-ground, and common fate—function as a formula for controlling focal points and visual rhythm.
格式塔理论提供了一组感知"定理"，描述大脑如何将视觉元素组织成统一整体。六大经典原则——相似性、接近性、连续性、闭合性、图形-背景与共同命运——作为控制焦点与视觉节奏的公式。
- Similarity / 相似性: elements of similar shape or colour are perceived as a group. / 形状或颜色相似的元素被视作一个群组。
- Proximity / 接近性: items placed near each other appear related. / 彼此靠近的物体显得有关联。
11. Leonardo’s Vitruvian Proportions | 达芬奇维特鲁威人体比例
Based on Vitruvius’s writings, Leonardo da Vinci codified an idealised set of human proportions that many artists still use as a base 'formula' for figure drawing. Key relationships include: height equals arm span; the length of the hand is 1/10 of total height; the distance from elbow to fingertip is 1/4 of total height.
基于维特鲁威的记述，达芬奇编纂了一套理想化的人体比例，至今仍是许多画家绘制人体的基础"公式"。关键关系包括：身高等于臂展；手长为总身高的 1/10；肘至指尖距离为总身高的 1/4。
12. Depth of Field & Aperture Simulation | 景深与光圈模拟
at fall outside the focal plane. The formula for circle of confusion guides this blur: c = |s – sf| / sf × f²/N(Sn – ding this optical law helps artists avoid uniform sharpness and create photographic depth.
绘制写实场景时，画家通过逐渐模糊焦平面外的物体来模拟浅景深。弥散圆公式指导此模糊程度：c = |s – sf| / sf × f²/N(Sn – f)，其中 sf 为对焦距离。虽然公式复杂，但理解此光学规律有助于艺术家避免均匀锐利，从而创造出摄影般的空间深度。
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