📚 Year 9 OCR Art: Formula & Theorem Quick Reference Guide | Year 9 OCR 艺术：公式定理速查手册
Art may seem free from rules, but mastering the visual language relies on a set of underlying 'formulas' and 'theorems' — colour mixing ratios, perspective vanishing points, composition grids, and proportion systems. This quick reference handbook gathers the essential principles you'll encounter in the Year 9 OCR Art curriculum, presented as clear, workable equations that you can apply directly in your sketchbook and final pieces.
艺术看似无拘无束，但要精通这门视觉语言，离不开一组隐藏的“公式”与“定理”——色彩的混合比例、透视的消失点、构图的网格法则、人体比例的系统。这本速查手册收集了 Year 9 OCR 艺术课程中的核心原理，并将它们表述成清晰可用的“方程式”，帮助你在素描本和最终作品中直接运用。
1. Colour Mixing Formulas | 色彩混合公式
rple, Yellow + Red = Orange. The exact shade depends on the ratio. For a muted tone, add a small amount of the complementary colour: e.g., Red + (1/10) Green → muted red-brown. A tint requires White, a shade needs Black, and a tone uses Grey.
三原色遵循减法混合规则。在绘画中，基本配方是：黄+蓝=绿，红+蓝=紫，黄+红=橙。精确色调取决于比例。要降低纯度，加入少量补色，例如：红+(1/10)绿 → 灰调红棕。制造浅色调需加白，暗色调加黑，而中间调需加灰。
- Tint Formula: Hue + White = Tint (lighter value) | 浅色调公式：色相 + 白 = 浅色调
- Shade Formula: Hue + Black = Shade (darker value) | 暗色调公式：色相 + 黑 = 暗色调
- Tone Formula: Hue + Grey = Tone (muted value) | 中间调公式：色相 + 灰 = 中间调
- Complementary Neutralising: Hue + Complement → natural grey/brown | 补色调和：色相 + 补色 → 自然灰/棕
2. Colour Harmony Theorems | 色彩和谐定理
The colour wheel theorems help predict harmony. Analogous colours sit side by side (e.g., Yellow, Yellow-Green, Green) and create serene, unified schemes. Complementary pairs sit opposite (Red & Green, Blue & Orange, Yellow & Purple) and generate maximum contrast. The 60-30-10 rule for balanced interiors can also guide composition: 60% dominant colour, 30% secondary, 10% accent.
色轮定理可预测和谐关系。邻近色相邻而坐（如黄、黄绿、绿），营造宁静统一的调子。补色对分处色轮两端（红与绿、蓝与橙、黄与紫），产生最大对比。室内设计中的 60-30-10 比例规则同样适用于构图：60% 主导色，30% 次要色，10% 强调色。
| Harmony Type | 和谐类型 | Formula | 公式 | Effect | 效果 |
|---|---|---|
| Analogous | Hue ± 30° on colour wheel | Calm, natural flow |
| Complementary | Hue + 180° | Vibrant, high contrast |
| Triadic | Hue + 120°, + 240° | Balanced but lively |
3. Perspective Formulas | 透视公式
vanishing point (VP) on the horizon line. The rule: all parallel lines receding into space converge at the VP. The scale factor formula for equally spaced objects: distance between first two objects ∕ stant depth ratio. Two-point perspective requires two VPs; vertical lines remain vertical, while horizontals angle towards the left or right VP.
一点透视在视平线上设一个消失点（VP）。法则：所有向深处延伸的平行线都汇聚于该点。等距物体的缩放系数公式为：第一、二物体间距与消失点到第一物体的距离之比为恒定深度比。两点透视需设左右两个消失点；垂直线保持垂直，水平线分别向左、右消失点倾斜。
Foreshortening index = actual size × (distance from VP)⁻¹ (approx.)
透视缩短指数 = 实际尺寸 × (与消失点距离)⁻¹ (近似)
- One-point Interior: VP at eye level, orthogonals radiate from VP. | 一点透视室内：消失点设于视高，直角线从消失点放射。
- Two-point Exterior: VPs on horizon, left and right. | 两点透视室外：消失点位于视平线左右两侧。
- Atmospheric Perspective: contrast ↓, detail ↓, colour cooler with distance. | 空气透视：距离增加时，对比度降低、细节减少、色彩偏冷。
4. Composition Rules | 构图法则
en Ratio (Φ ≈ 1.618) gives a more dynamic proportion: place the main subject at the spiral' rem states that arranging key elements in an implied triangle enhances stability and flow.
三分法将画面分成 3×3 网格，交点处视觉权重最强。黄金分割（Φ≈1.618）带来更具动态的比例：将主体置于螺旋线的中心。三角构图定理指出，将关键元素布置成一个隐含的三角形能增强稳定感和视觉流动。
Focal Point Placement = Grid intersection (3³) OR Golden Spiral focus (Φ rectangle)
焦点定位 = 网格交叉点（三分点）或黄金螺旋焦点（Φ 矩形）
5. Human Figure Proportion Theorems | 人体比例定理
The classical canon uses head lengths: an adult body ≈ 7.5– es that every pose has a dominant curve running through the spine and limbs; capturing it first ensures dynamic movement.
古典准则以头长为单位：成年人体约等于 7.5–8 个头高。关键标记：肩宽≈2 头宽，骨盆≈1.5 头宽。双眼位于身高一半处。在速写中，动态线定理指出每个姿势都有一条贯穿脊椎与四肢的主导曲线；优先捕捉它能保证动态感。
| Body Part | 部位 | Proportion (heads) | 比例（头长） |
|---|---|
| Total height | 7.5–8 |
| Arms (shoulder to fingertip) | 3–3.5 |
| Legs (hip to sole) | 4–4.5 |
6. Shading and Lighting Equations | 明暗与光线公式
The value scale from 1 (white) to 9 (black) maps the light– Reflected light formula: shadow side lightens near the surface, obeying the law: reflected light intensity = surface albedo × ambient light.
从 1（白）到 9（黑）的明度标尺描绘了光与影的过渡。明暗交界线定理：圆转形体上最暗处不在边缘，而在光线与阴影交界的明暗交界面。反光公式：阴影侧靠近表面的部分会因环境光而提亮，遵循：反光强度 = 表面反射率 × 环境光。
- Highlight → Light → Halftone → Core Shadow → Reflected Light → Cast Shadow
- 高光 → 亮部 → 半调子 → 明暗交界线 → 反光 → 投影
Light angle rule: surfaces facing the light source are brightest; surfaces angled away darken proportionally to cos(θ), where θ is the angle between surface normal and light direction.
光线入射角规则：朝向光源的表面最亮；偏离光源的表面随法线与光线夹角 θ 变暗，遵循 cos(θ) 关系。
7. Texture and Pattern Principles | 纹理与图案定理
rkness. Pattern theorem: repetition with variation creates rhythm; alternating grid units follow the rule: A-B-A-B or A-A-B-A-A-B. Rotation, reflection, and scaling of a motif generate complex tessellations.
纹理可以是实际的（触觉的）或隐含的（视觉的）。笔触排列公式：排线密度 = 感知的明暗度。图案定理：重复中带有变化产生节奏；交替网格单元遵循 A-B-A-B 或 A-A-B-A-A-B 法则。基本母题的旋转、反射和缩放可生成复杂的镶嵌图案。
8. Spatial and Depth Cues | 空间与深度线索
of depth. Size constancy theorem: objects farther away are drawn smaller, following scale ∝ on plane: objects closer to the bottom edge appear nearer; those higher up appear farther.
深度方程式：重叠 + 相对大小 + 画面中位置 + 线性透视 + 空气透视 = 令人信服的深度错觉。大小恒常定理：远处物体画得较小，遵循 比例 ∝ 1/与观者距离。画面位置：靠近底边的物体显得更近；高处物体显得更远。
9. Form and Structure Formulas | 形体与结构公式
Basic forms — cube, sphere, cylinder, cone, pyramid — underpin all complex objects. The constructive drawing theorem: any object can be simplified into these primitives. Cross-contour lines describe volume; they wrap around the form like latitude lines. The formula for an ellipse in perspective: the minor axis aligns with the centre line of the cylinder, and the degree (opening) increases as it moves away from eye level.
基本形体——立方体、球体、柱体、锥体、棱锥——是一切复杂物体的基础。结构素描定理：任何物体都可简化为这些基本形体。轮廓交叉线描绘体积，像纬线一样包裹形体。透视中的椭圆公式：短轴与圆柱体中轴线对齐，开口度（椭圆的开张程度）随远离视平线而增大。
10. Movement and Balance Theorems | 动态与平衡定理
(the lever principle). The motion theorem: diagonal lines, repeated curves, and blurred edges suggest movement. The visual weight equation: perceived weight = size × contrast × colour intensity × detail density.
平衡并不等于对称。不对称布局可通过调整视觉重量实现均衡：一个小面积的暗色块能与大面积的亮色区域相抗衡（杠杆原理）。动态定理：斜线、重复曲线和模糊边缘能暗示运动感。视觉重量方程：感知重量 = 尺寸 × 对比度 × 色彩强度 × 细节密度。
11. Creative Problem-Solving Equations | 创意问题解决方程
il sketches + Artist reference = Coherent personal response. Another useful equation: Risk-taking = (Unfamiliar technique + Personal interpretation) / Fear of mistakes.
在 OCR 艺术中，评估聚焦创作过程：实验 + 完善 = 进步。灵感生成公式：思维导图 + 构图小稿 + 艺术家参考 = 连贯的个性化回应。另一条实用方程：冒险精神 = (不熟悉的技法 + 个人解读) / 对犯错的恐惧。
- Develop → Refine → Reflect → Record → Present | 发展 → 完善 → 反思 → 记录 → 呈现
- Annotate: What? How? Why? What next? | 注释四问：是什么？怎么做的？为什么？下一步？
12. Evaluation and Reflection Formulas | 评估与反思公式
elf-assessment theorem: Strengths + Weaknesses + Next Steps = Meaningful critique. Use the 'WWW/EBI' formula: What Went Well / Even Better If. When analysing an artist's work, apply the Context–Content–Form–Meaning formula: CCFM = full understanding.
自我评估定理：优势 + 不足 + 下一步 = 有意义的评析。使用“WWW/EBI”公式：做得好的地方 / 如果……还能更好。分析艺术作品时，运用语境–内容–形式–意义公式：CCFM 带来全面理解。
| Element | 元素 | Reflective Prompt | 反思提示 |
|---|---|
| Context | When, where, by whom? Social/cultural influences? |
| Content | Subject matter, symbols, narrative. |
| Form | Materials, techniques, composition, colour, line. |
| Meaning | Mood, message, viewer's reaction, artist's intention. |
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