📚 GCSE Edexcel Art: Formula & Theorem Quick Reference Handbook | GCSE Edexcel 艺术：公式定理速查手册
This quick-reference guide brings together the essential “formulas” and principles that underpin GCSE Edexcel Art & Design. While art may not be built on equations in the traditional sense, every successful composition relies on repeatable structures, ratios, colour relationships, and spatial rules. Understanding these will help you justify your creative decisions in annotation, planning, and final outcomes, and meet the assessment objectives with confidence.
这本速查手册汇集了支撑 GCSE Edexcel 艺术与设计的基础“公式”与原理。虽然艺术在传统意义上不是靠方程式建立的，但每一件成功的作品都依赖于可重复的结构、比例、色彩关系和空间规则。理解这些将帮助你在注释、规划和最终作品中自信地说明自己的创作决策，并更好地达成评估目标。
1. The Colour Wheel Formula | 色轮公式
The 12‑part colour wheel is built from three primaries (red, yellow, blue), three secondaries (orange, green, violet), and six tertiaries. The formula for mixing any secondary is: Primary A + Primary B = Secondary (e.g. Red + Yellow = Orange). Tertiaries are mixed by combining a primary with its adjacent secondary.
12色色轮由三种原色（红、黄、蓝）、三种间色（橙、绿、紫）和六种复色构成。混合间色的公式是：原色A + 原色B = 间色（例如 红 + 黄 = 橙）。复色则由一种原色与相邻的间色混合而成。
Complementary colours sit opposite each other on the wheel. The theorem states that when placed side by side, complements create maximum contrast and vibrance; when mixed, they neutralise each other to produce browns and greys. This underpins colour theory in painting and design.
互补色在色轮上正对彼此。该定理表明：互补色并置时产生最强的对比与鲜亮感；混合时则相互中和，生成褐色与灰色。这是绘画与设计中色彩理论的基础。
| Harmony | Formula | 色彩和谐 | 公式 |
| Complementary | Colour + Opposite on wheel | 互补 | 色轮上相对的颜色 |
| Analogous | 3–4 colours side by side | 类似色 | 相邻的3–4种颜色 |
| Triadic | 3 colours evenly spaced (120° apart) | 三角色 | 均匀间隔的3种颜色（相隔120°） |
2. Golden Ratio in Composition | 构图中的黄金比例
The golden ratio (Phi, approximately 1:1.618) is a proportional relationship found in nature and classical art. When applied to a rectangle, the longer side is roughly 1.618 times the shorter side. This creates a visually pleasing balance that guides the eye naturally across the composition.
黄金比例（φ，约 1:1.618）是一种在自然和古典艺术中存在的比例关系。应用于矩形时，长边约为短边的1.618倍。这创造出视觉上令人愉悦的平衡，引导视线自然地在画面上移动。
To construct a golden section in a composition, divide a line so that the ratio of the whole line (A+B) to the larger segment (A) equals the ratio of the larger segment (A) to the smaller segment (B). In formula form: (A+B)/A = A/B. Many artists place the focal point at one of the golden section intersections to achieve dynamic tension.
在构图中构造黄金分割：将一条线分割，使整条线(A+B)与较长段(A)的比值等于较长段(A)与较短段(B)的比值。公式形式：(A+B)/A = A/B。许多艺术家将焦点放置在黄金分割交点之一，以获得动态张力。
3. Rule of Thirds | 三分法则
A simplified version of the golden ratio, the rule of thirds divides the picture plane into nine equal rectangles using two horizontal and two vertical lines. Placing key elements along these lines or at their intersections creates a balanced, engaging composition. The formula: divide the height and width by 3, and align subjects with the 1/3 or 2/3 lines.
作为黄金比例的简化版，三分法则用两条水平线和两条垂直线将画面分成九个相等的矩形。将关键元素沿这些线或它们的交点放置，会创造出平衡且引人入胜的构图。公式：将高度和宽度除以3，把主体对齐在1/3或2/3的线上。
In portraiture, placing the eyes on the upper horizontal third is a widely used convention. For landscapes, the horizon often sits on the lower or upper third, never exactly in the centre unless symmetry is intentional.
在肖像画中，将眼睛放置在上方水平三分之一处是一种广泛使用的惯例。对于风景画，地平线通常位于下方或上方三分之一处，除非有意追求对称，否则绝不正中央。
4. One‑Point Perspective Formula | 一点透视公式
One‑point perspective uses a single vanishing point on the horizon line. All receding parallel lines (orthogonals) converge at that point. The formula for positioning an object in depth: the apparent size of an object halves as the distance from the viewer doubles. This can be expressed as: Apparent Size ∝ 1/Distance.
一点透视在地平线上使用一个单独的消失点。所有后退的平行线（正交线）汇聚于该点。在深度上放置物体的公式：物体离观者距离加倍时，其表观尺寸减半。可表示为：表观尺寸 ∝ 1/距离。
To draw a grid floor in perspective, first draw the base line, then connect its equally spaced points to the vanishing point. Next, draw a diagonal across the floor plane; its intersections with the receding lines mark where transverse lines should be drawn. This ensures mathematically correct foreshortening.
要在透视中画出网格地面，先画基线，然后将其等分点连接到消失点。接着在地面平面上画一条对角线，它与各后退线的交点即是应画横线的位置。这样能确保缩形在数学上准确。
5. Two‑Point Perspective and the Cone of Vision | 两点透视与视锥
Two‑point perspective uses two vanishing points on the horizon line. The formula for the angle between receding planes relies on the concept of the station point. Usually the vanishing points are placed so that the angle between them from the station point is 90°. Outside this 90° cone of vision, distortion becomes noticeable, so keep important forms within this cone.
两点透视在地平线上使用两个消失点。后退平面之间角度的公式依赖于视点（站点）的概念。通常两个消失点的位置从站点看去彼此成90°角。超出这个90°视锥范围，变形会很明显，因此要把重要形体保持在这个视锥内。
To construct two‑point perspective accurately: draw a horizon, place two vanishing points suitably far apart, then project lines from both vanishing points to define the corners of a block. Vertical lines remain perfectly vertical and are not foreshortened.
要准确构建两点透视：画出地平线，将两个消失点设置在合适的远距离处，然后从两个消失点分别引出线条以定义块面的转角。垂直线保持完全竖直，不产生缩形。
6. Human Proportion: The Canon of 8 Heads | 人体比例：八头身法则
The classical canon of human proportion divides the body height into 8 units of the head height. Landmarks: 0 heads = top of head; 1 head = chin; 2 heads = nipples/armpit; 3 heads = navel; 4 heads = pubic bone; 5 heads = mid‑thigh; 6 heads = bottom of knees; 7 heads = mid‑calf; 8 heads = soles of feet. Arms extend to mid‑thigh (just above 5 heads).
古典人体比例法则将身高分成头高的8个单位。标志点：0头身 = 头顶；1头身 = 下巴；2头身 = 乳头/腋窝；3头身 = 肚脐；4头身 = 耻骨；5头身 = 大腿中部；6头身 = 膝盖下方；7头身 = 小腿中部；8头身 = 脚底。手臂延伸至大腿中部（刚过5头身）。
In figure drawing, the pubic bone marks the exact midpoint of the body. The width of the shoulders is approximately 2 head widths for an adult male. When drawing a face, the eyes are placed halfway between the top of the head and the chin – a fundamental proportion often overlooked.
在人体素描中，耻骨是身体的精确中点。成年男性的肩宽约为2个头宽。画脸时，眼睛位于头顶到下巴的正中间——这是一个常被忽视的基本比例。
7. Value and Tonal Scales | 明度与色调层次
Value refers to the lightness or darkness of a tone. A standard 9‑step value scale ranges from pure white (value 1) to pure black (value 9). The formula for creating a middle value is to mix equal optical quantities of black and white, but because black pigment is stronger, in paint a middle grey requires more white than black.
明度指色调的亮暗程度。一个标准的9阶明度尺从纯白（明度1）到纯黑（明度9）。创造中明度的公式是等量混合黑白的光学量，但由于黑色颜料着色力更强，在绘画中中灰需要比黑色更多的白色。
The chiaroscuro method suggests using a full value range to model form. A key theorem: the highlight on a sphere is not at the edge but between the terminator and the light source, while the reflected light on the shadow side should never be lighter than the darkest tone of the lit side.
明暗对照法强调使用全范围明度来塑造形体。一条关键定理：球体上的高光不在边缘，而位于明暗交界线与光源之间，同时阴影一侧的反光绝不应亮过受光面最暗的调子。
| Value | Description | 明度 | 描述 |
| 1 | White / Highlight | 白 / 高光 | 最亮 |
| 5 | Middle grey | 中灰 | 中间调 |
| 9 | Black / Deep shadow | 黑 / 深阴影 | 最暗 |
8. Mixing Pigments: Subtractive Colour Mixing Rules | 颜料混合：减色混合规则
In paint, colour mixing is subtractive: pigments absorb (subtract) certain wavelengths and reflect others. The primaries for pigment are cyan, magenta, and yellow, though artists often use red, yellow, blue. The mixing formulas: Cyan + Magenta = Blue; Cyan + Yellow = Green; Magenta + Yellow = Red. All three together yield a dark neutral.
在颜料中，色彩混合是减色的：颜料吸收（减去）特定波长而反射其他波长。颜料的原色是青、品红和黄，但艺术家常用红、黄、蓝。混合公式：青+品红=蓝；青+黄=绿；品红+黄=红。三者混合得到深暗的中性色。
To desaturate a colour (make it less intense), add a small amount of its complementary colour. This is more controlled than adding black, which can deaden the hue. The formula: Hue + Complement → lowered saturation. A Tint is created by adding white; a Shade by adding black; a Tone by adding grey (black + white).
要降低色彩的饱和度（减弱鲜艳度），加入少量它的互补色。这比加黑色更可控，后者容易使色相沉闷。公式：色相 + 互补色 → 饱和度降低。加白得到浅调（Tint）；加黑得到深调（Shade）；加灰（黑+白）得到浊调（Tone）。
9. Texture and Pattern Repeat Formulas | 肌理与图案重复公式
A regular pattern follows a repeat formula. Basic repeats include: Block repeat (grid of identical units), Half‑drop repeat (every other row shifted by half the width of the motif), and Mirror repeat (each unit is reflected horizontally or vertically). The formula for a half‑drop: Row Y = Row 1 shifted right by W/2, where W is motif width.
规则的图案遵循重复公式。基础重复方式包括：平接（方格重复相同单元）、半错位（每隔一列错开图案宽度的一半）和镜像重复（每个单元水平或垂直翻转）。半错位的公式：第Y行 = 第1行右移W/2，其中W为图案宽度。
In texture creation, the visual weight of a mark depends on its size, spacing, and value. A simple formula: Close, dark, thick marks yield a dense texture; sparse, light, thin marks yield an open, airy texture. Contrast in texture can create focal points without changing colour.
在肌理营造中，笔触的视觉重量取决于其大小、间距和明度。一个简单公式：密、暗、粗的笔触产生紧密的肌理；疏、亮、细的笔触产生疏松透气的肌理。肌理上的对比可以在不改变颜色的情况下制造焦点。
10. Grid Enlargement Method | 网格放大法
To accurately enlarge a smaller sketch or photograph, use a proportion grid. The formula: if the original width Wₒ and the desired width W_d, the scale factor S = W_d / Wₒ. Apply S to all measurements. Draw a grid of equally spaced squares on the original and a corresponding grid on the larger surface with squares scaled by S.
要准确放大一幅小素描或照片，可使用比例网格。公式：原宽度Wₒ，目标宽度W_d，则比例因子 S = W_d / Wₒ。将所有尺寸乘以S。在原图上画等距方格网，在放大表面上画相应的方格网，方格边长乘以S。
For example, to enlarge a 10 cm×15 cm image to 30 cm×45 cm, S = 3. Draw a 1 cm grid on the original and a 3 cm grid on the enlargement. Then copy the content square by square, maintaining the position of lines within each cell. This ensures proportional accuracy.
例如，将10 cm×15 cm的图像放大到30 cm×45 cm，S = 3。在原图上画1 cm网格，在放大面上画3 cm网格。然后逐格复制内容，保持每格内线条位置对应。这确保了比例准确。
11. Printmaking Registration and Inking Ratios | 版画对版与墨量比例
In relief printing (lino or woodcut), the depth of cut influences ink transfer. The formula for even inking: use a thin, even film of ink. A common starting ratio for oil‑based ink extender is 10% extender to 90% ink for smooth papers. For reduction printing, plan colour from lightest to darkest, as each layer covers part of the previous.
在凸版印刷（麻胶版或木刻）中，刻刀深度影响油墨传递。均匀上墨的公式：使用薄而均匀的墨层。对于油性油墨连结料，适合光滑纸张的起始比例是10%连结料加90%油墨。制作减版版画时，从最浅色安排到最深色，因为每一层都会覆盖前一层的一部分。
Registration requires a jig or pin system. The simple formula: fix the paper along one edge and drop the block into a corner registration device, ensuring each colour prints exactly in the same position. A mis‑registration of even 1 mm can blur the image.
对版需要一个定位工具（印刷夹或钉销）。简单公式：将纸张沿一边固定，将版放入角落定位装置，确保每种颜色都印在完全相同的位置。哪怕偏移1毫米都可能使图像模糊。
12. Digital Resolution and File Settings | 数字分辨率与文件设置
For digital artwork, resolution is measured in pixels per inch (ppi). The formula for required pixel dimensions: Width in pixels = Print width (inches) × ppi. For screen display, 72 ppi is sufficient; for high‑quality art prints, use 300 ppi. Colour mode: RGB for screen, CMYK for printing. DPI (dots per inch) refers to printer output and is not the same as ppi.
对于数字艺术作品，分辨率以每英寸像素数（ppi）衡量。所需像素尺寸的公式：宽像素数 = 打印宽（英寸）× ppi。用于屏幕显示72 ppi即可；高质量艺术打印使用300 ppi。色彩模式：屏幕用RGB，打印用CMYK。dpi（每英寸点数）是指打印机的输出，与ppi不同。
When saving files for your portfolio, follow the formula: high resolution master file (TIFF or PSD) → flattened JPEG copy at quality 10–12 for submission. Always keep a working file with layers. The aspect ratio (width ÷ height) should remain constant when resizing to avoid distortion. For Edexcel digital submissions, check the precise file format and size guidelines.
为作品集保存文件时，遵循公式：高分辨率主文件（TIFF或PSD）→ 提交用拼合JPEG副本，品质10–12。始终保留带图层的工作文件。在调整大小时保持宽高比（宽÷高）不变以避免变形。对于Edexcel数字提交，请查核确切的文件格式和大小要求。
13. The Assessment Objectives as a Formula for Success | 评估目标：成功的公式
Edexcel GCSE Art & Design is assessed against four Assessment Objectives, each weighted equally at 25%. Think of them as the ingredients of a successful project: AO1 (Develop) = gather, research, explore artists; AO2 (Refine) = experiment, select media, take risks; AO3 (Record) = draw, photograph, annotate; AO4 (Present) = final outcome that connects to your journey. No single AO can be neglected.
Edexcel GCSE艺术与设计根据四项评估目标评分，每项各占25%。把它们看作成功项目的配方：AO1（发展）= 收集、调研、探索艺术家；AO2（提炼）= 实验、选择媒介、冒险尝试；AO3（记录）= 绘画、摄影、注释；AO4（呈现）= 与创作历程相连的最终成果。任何一项都不能忽视。
The formula for a high mark: (Strong AO1) + (Inventive AO2) + (Thorough AO3) + (Resolved AO4) = Coherent portfolio. Every piece of annotation should explicitly reference which AO it addresses, demonstrating your understanding of the process.
获得高分的公式：（扎实的AO1）+（有创意的AO2）+（彻底的AO3）+（完善的AO4）= 连贯的作品集。每一段注释都应明确提及它对应的是哪个AO，展示你对创作过程的理解。
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