📚 Year 9 WJEC Art: Formula & Theorem Quick Reference Guide | WJEC 九年级艺术：公式定理速查手册
This quick reference guide compiles the essential formulas and theorems that underpin many artistic techniques studied in Year 9 WJEC Art and Design. From the mathematics of perspective to the geometry of composition and the science of colour mixing, these principles help students create visually compelling artwork with confidence.
本速查手册汇编了 WJEC 九年级艺术与设计课程中支撑多种艺术技法的基础公式与定理。从透视数学到构图几何，再到色彩混合科学，这些原理帮助学生自信地创作出视觉上引人入胜的作品。
1. The Golden Ratio (φ) in Composition | 构图中的黄金比例 (φ)
The Golden Ratio, approximately 1.618, has been used by artists for centuries to create balanced, naturally pleasing compositions. When a line is divided into two parts such that the ratio of the whole line to the longer part equals the ratio of the longer part to the shorter part, the division point is known as the golden section.
φ = (1 + √5) ÷ 2 ≈ 1.618
黄金比例（约 1.618）几个世纪以来一直被艺术家用于创造平衡而自然的构图。当一条线段被分成两部分，使得整条线与较长部分的比值等于较长部分与较短部分的比值时，分割点即为黄金分割。将主体放置在黄金螺旋或黄金矩形的关键点上，能显著增强视觉吸引力。
2. Rule of Thirds Grid Formula | 三分法网格公式
The Rule of Thirds is a fundamental compositional guideline that divides the canvas into nine equal parts using two equally spaced horizontal lines and two equally spaced vertical lines. Placing focal points at the intersections creates a dynamic and balanced image.
1/3 + 1/3 + 1/3 = 1
三分法是基本的构图指导法则，它将画面用两条等距的水平线和两条等距的垂直线分成九个相等部分。将视觉焦点放置在线条交叉点上，能营造出动感而平衡的图像。网格划分公式直观地表达了画面被三等分后各部分之和等于整体。
3. One-Point Perspective: Vanishing Point Equation | 单点透视：消失点方程
In one-point perspective, all receding parallel lines (orthogonals) converge at a single vanishing point (VP) on the horizon line. The apparent size of an object decreases as its distance from the viewer increases.
Object height ∝ 1 / Distance
在单点透视中，所有向远方延伸的平行线（正交线）汇聚于地平线上的一个消失点（VP）。物体的表观尺寸随观者距离的增加而减小，其关系可表示为：物体高度 ∝ 1 / 距离。这意味着当距离加倍时，物体的表观高度约减半。
4. Two-Point Perspective: Distance Factor | 两点透视：距离因子
When an object is rotated, two-point perspective uses two vanishing points on the horizon. The distance between the two vanishing points depends on the viewer's distance and the angle of view. A simplified formula is:
VP₁VP₂ Distance = 2 × d × tan(θ/2)
当物体旋转时，两点透视在地平线上使用两个消失点。两消失点之间的距离取决于观者距离和视角。简化公式为：VP₁VP₂ 间距 = 2 × d × tan(θ/2)。这里 d 代表观者到画面的距离，θ 为观察角度。
5. Colour Mixing: Primary Equations | 色彩混合：原色公式
In traditional colour theory, secondary colours are created by mixing primary colours. The basic subtractive mixing rules for paints can be remembered through these equations:
Red + Yellow = Orange
Blue + Yellow = Green
Red + Blue = Purple
在传统色彩理论中，二次色是由原色混合而成的。颜料（减法混合）的基本混色规则可以通过以下等式记忆：红 + 黄 = 橙、蓝 + 黄 = 绿、红 + 蓝 = 紫。所有其他中间色调均可通过改变这些混合比例得到。
6. Tonal Value Scale Formula | 明度等级公式
An even tonal scale from pure white to pure black is essential for shading and creating depth. A ten-step value scale can be represented numerically, where 0 is white and 9 is black. The value at any step n is:
Vₙ = n / 9 (n = 0, 1, 2, ..., 9)
从纯白到纯黑的均匀明度等级对于表现明暗和立体感至关重要。十级明度标尺可以用数字表示，其中 0 为白、9 为黑。任一级别 n 的明度值为：Vₙ = n/9（n = 0, 1, 2, …, 9）。明度 5 对应中等灰，即 50% 灰。
7. Complementary & Triadic Colour Harmonies | 互补与三角色彩和谐
Colour harmony relies on the colour wheel. Complementary colours sit exactly 180° apart. A triadic scheme uses three colours equally spaced by 120°:
Complementary: H₂ = H₁ + 180°
Triadic: H₂ = H₁ + 120°, H₃ = H₁ + 240°
色彩和谐依赖于色轮。互补色在色轮上正好相隔 180°。三角色方案使用三个等距 120° 的颜色：互补公式 H₂ = H₁ + 180°；三角公式 H₂ = H₁ + 120°，H₃ = H₁ + 240°。这些角度关系能确保配色具有天然的统一感。
8. Grid Method Scaling Formula | 网格放大法缩放公式
riginal image has dimensions W₁ × H₁ and you enlarge it to W₂ × H₂, the scale factor S is:
S = W₂ ÷ W₁
在将参考图像转移到更大的画布上时，网格法能确保比例准确。如果原始图像尺寸为 W₁ × H₁，并放大至 W₂ × H₂，则缩放因子 S = W₂ ÷ W₁。新画布上每个网格的边长 = 参考网格边长 × S。同样 S 也可用于高度，只要保持原始宽高比。
9. Human Figure Proportions: 8-Head Canon | 人体比例：八头身法则
In classical figure drawing, an idealised adult human height is often divided into 8 head lengths. This canon provides a reliable guide for placing body landmarks. The total height H relates to head length h:
H = 8 × h
在古典人物绘画中，理想化的成人身高通常分为 8 个头长。这一法则为确定身体各部位位置提供了可靠指引。总身高 H 与头长 h 的关系为：H = 8 × h。其中肩宽约 2h，耻骨位于第 4 头长处分界，膝盖约在第 6 头长处。
10. Visual Balance Weight Equation | 视觉平衡重量公式
In a composition, elements carry different visual weights. A small, highly saturated area can balance a large, dull area. A simplified visual weight equation to consider is:
Visual Weight ∝ Size × Contrast × Colour Intensity
在构图中，不同元素携带不同的视觉重量。一个面积小但高饱和的区域可以平衡一个面积大但灰暗的区域。一个简化的视觉重量公式为：视觉重量 ∝ 尺寸 × 对比度 × 色彩强度。通过调整这些变量，艺术家可以创造出令人愉悦的动态平衡。
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